### Related

##### rk

g:10;

Points:rk(-g,y,0,[t,0...

Calculate

? rk;

Calculate

##### rk

pts:rk(y-(x-2)^2, y, ...

Calculate

##### rk

sol: rk([4-x^2-4*y^2,...

table_form(sol, colum...

Calculate

##### rk-tan

sol: rk((x*y^2)/2 + (...

Calculate

##### rk

a:rk([-x,y],[y,z],[0,...

Calculate

##### rk

sol: rk([4-x^2-4*y^2,...

sol;

Calculate

##### rk

rk(-2*x^3+12*x^2-20*x...

Calculate

##### rk

g:10;

Points:rk([V,-g],[y, ...

Calculate

##### rk

g:10;

rk([V,-g],[y, V],[0,1...

Calculate

### rk

Run Example
```(%i1)gpot: 4;
(%o1)                                  4
(%i2) dxdt: vx;
(%o2)                                 vx
(%i3) dvxdt: -x/(x^2+y^2)^((gpot+1)/2);
x
(%o3)                           - ------------
2    2 5/2
(y  + x )
(%i4) dydt: vy;
(%o4)                                 vy
(%i5) dvydt: -y/(x^2+y^2)^((gpot+1)/2);
y
(%o5)                           - ------------
2    2 5/2
(y  + x )
(%i6) x0: 1;
(%o6)                                  1
(%i7) y0: 0;
(%o7)                                  0
(%i8) vx0: 0;
(%o8)                                  0
(%i9) vy0: 0.8;
(%o9)                                 0.8
(%i10) points: rk([dxdt,dydt,dvxdt,dvydt],[x,y,vx,vy],[x0,y0,vx0,vy0],[t,0,27,0.2]);
(%o10) [[0, 1, 0, 0, 0.8], [0.2, 0.97994402898821, 0.15892333797882,
- 0.20106571052834, 0.78376473020946],
[0.4, 0.9191251104626, 0.31115175589081, - 0.40884860122868,
0.73198442316315], [0.6, 0.81542552825771, 0.44864792902243,
- 0.63148779116339, 0.63363613400496],
[0.8, 0.66479046167805, 0.55980839340965, - 0.88074085706835,
0.46172735890912], [1.0, 0.46013622929416, 0.62401577804146,
- 1.17623723149005, 0.14344974384913],
[1.2, 0.18928641937503, 0.59157174929807, - 1.547526578148681,
- 0.60994609678085], [1.4, - 0.14351602991004, 0.20333268046667,
2.207759724738516, - 9.374544211221252],
[1.6, 1.297647125294126, - 3.068808437402134, 7.193084135025295,
- 16.24416590959128], [1.8, 2.736235153012654, - 6.317573805762186,
7.192895583218034, - 16.24372327285756],
[2.0, 4.174812144974642, - 9.566313564697165, 7.192879109846423,
- 16.24368535725922], [2.2, 5.613387502220808, - 12.81504957243489,
7.19287523687717, - 16.24367649725376],
[2.4, 7.051962393128261, - 16.06378451492054, 7.192873879830318,
- 16.24367340232824], [2.6, 8.490537102310325, - 19.31251904332768,
7.192873285713834, - 16.24367204990424],
[2.8, 9.929111726293336, - 22.56125337790853, 7.192872985472651,
- 16.24367136731308], [3.0, 11.36768630509667, - 25.80998760981965,
7.192872817693124, - 16.24367098622006],
[3.2, 12.80626085773231, - 29.05872178231358, 7.192872716682008,
- 16.24367075694365], [3.4, 14.24483539417084, - 32.30745591805277,
7.192872652270049, - 16.24367061082017],
[3.6, 15.68340992004987, - 35.55619002984204, 7.192872609274556,
- 16.24367051332441], [3.8, 17.12198443875182, - 38.80492412535953,
7.192872579485374, - 16.24367044579944],
[4.0, 18.56055895240577, - 42.05365820943612, 7.192872558197465,
- 16.24367039755943], [4.2, 19.99913346240614, - 45.30239228523444,
7.192872542582189, - 16.24367036218315],
[4.4, 21.43770796969712, - 48.55112635489532, 7.192872530869187,
- 16.2436703356533], [4.600000000000001, 22.87628247493649,
- 51.79986041990978, 7.192872521911807, - 16.24367031536882],
[4.800000000000001, 24.3148569785939, - 55.04859448134208, 7.192872514945083,
- 16.24367029959496], [5.0, 25.75343148101189, - 58.29732853996836,
7.192872509445366, - 16.24367028714451],
[5.2, 27.19200598244511, - 61.54606259636539, 7.192872505045977,
- 16.24367027718635], [5.4, 28.63058048308598, - 64.79479665096903,
7.192872501484943, - 16.24367026912679],
[5.600000000000001, 30.06915498308214, - 68.04353070411359, 7.192872498571712,
- 16.2436702625341], [5.800000000000001, 31.50772948254837,
- 71.29226475605897, 7.192872496165432, - 16.24367025708917],
[6.0, 32.946303981575, - 74.54099880700967, 7.192872494160456,
- 16.24367025255272], [6.2, 34.3848784802339, - 77.78973285712839,
7.192872492476496, - 16.2436702487429],
[6.4, 35.82345297858284, - 81.03846690654586, 7.192872491051793,
- 16.24367024551987], [6.600000000000001, 37.26202747666867,
- 84.28720095536814, 7.192872489838313, - 16.24367024277488],
[6.800000000000001, 38.70060197452971, - 87.53593500368193, 7.19287248879832,
- 16.24367024042247], [7.0, 40.13917647219756, - 90.78466905155874,
7.192872487901885, - 16.2436702383949],
[7.2, 41.57775096969843, - 94.03340309905791, 7.192872487125069,
- 16.24367023663799], [7.4, 43.01632546705426, - 97.28213714622905,
7.192872486448567, - 16.24367023510803],
[7.600000000000001, 44.45489996428349, - 100.5308711931139, 7.192872485856696,
- 16.24367023376953], [7.800000000000001, 45.89347446140172,
- 103.7796052397477, 7.192872485336624, - 16.24367023259346],
[8.0, 47.33204895842222, - 107.0283392861605, 7.192872484877786,
- 16.2436702315559], [8.200000000000001, 48.77062345535633,
- 110.2770733323779, 7.19287248447143, - 16.24367023063706],
[8.4, 50.2091979522138, - 113.5258073784221, 7.19287248411026,
- 16.24367022982042], [8.6, 51.64777244900304, - 116.774541424312,
7.192872483788166, - 16.24367022909216],
[8.800000000000001, 53.08634694573133, - 120.0232754700641, 7.192872483500005,
- 16.24367022844064], [9.0, 54.52492144240501, - 123.2720095156927,
7.192872483241422, - 16.24367022785602],
[9.200000000000001, 55.96349593902962, - 126.5207435612104, 7.192872483008717,
- 16.24367022732992], [9.4, 57.40207043561001, - 129.7694776066281,
7.192872482798733, - 16.24367022685519],
[9.600000000000001, 58.84064493215045, - 133.0182116519555, 7.192872482608763,
- 16.24367022642573], [9.800000000000001, 60.2792194286547,
- 136.2669456972011, 7.192872482436479, - 16.24367022603626],
[10.0, 61.71779392512609, - 139.5156797423724, 7.192872482279868,
- 16.24367022568223], [10.2, 63.15636842156758, - 142.7644137874761,
7.192872482137189, - 16.2436702253597],
[10.4, 64.5949429179818, - 146.0131478325181, 7.192872482006926,
- 16.24367022506525], [10.6, 66.03351741437109, - 149.2618818775038,
7.192872481887758, - 16.24367022479588],
[10.8, 67.47209191073756, - 152.510615922438, 7.192872481778528,
- 16.24367022454898], [11.0, 68.9106664070831, - 155.7593499673248,
7.19287248167822, - 16.24367022432225],
[11.2, 70.3492409034094, - 159.0080840121681, 7.192872481585944,
- 16.24367022411368], [11.4, 71.78781539971797, - 162.2568180569714,
7.19287248150091, - 16.24367022392148],
[11.6, 73.2263898960102, - 165.5055521017377, 7.192872481422421,
- 16.24367022374408], [11.8, 74.66496439228735, - 168.7542861464699,
7.192872481349861, - 16.24367022358008],
[12.0, 76.10353888855052, - 172.0030201911705, 7.192872481282679,
- 16.24367022342824], [12.2, 77.54211338480074, - 175.2517542358419,
7.192872481220387, - 16.24367022328745],
[12.4, 78.98068788103896, - 178.5004882804861, 7.192872481162547,
- 16.24367022315673], [12.6, 80.41926237726602, - 181.7492223251052,
7.192872481108768, - 16.24367022303519],
[12.8, 81.85783687348271, - 184.9979563697008, 7.192872481058701,
- 16.24367022292203], [13.0, 83.29641136968974, - 188.2466904142745,
7.192872481012031, - 16.24367022281656],
[13.2, 84.73498586588774, - 191.4954244588278, 7.192872480968473,
- 16.24367022271812], [13.4, 86.17356036207731, - 194.7441585033622,
7.192872480927774, - 16.24367022262614],
[13.6, 87.61213485825901, - 197.9928925478787, 7.192872480889703,
- 16.2436702225401], [13.8, 89.05070935443335, - 201.2416265923786,
7.192872480854049, - 16.24367022245953],
[14.0, 90.48928385060079, - 204.4903606368629, 7.192872480820626,
- 16.243670222384], [14.2, 91.92785834676174, - 207.7390946813325,
7.192872480789261, - 16.24367022231312],
[14.4, 93.36643284291661, - 210.9878287257884, 7.192872480759799,
- 16.24367022224654], [14.6, 94.80500733906577, - 214.2365627702314,
7.192872480732095, - 16.24367022218394],
[14.8, 96.24358183520955, - 217.4852968146622, 7.192872480706023,
- 16.24367022212502], [15.0, 97.68215633134828, - 220.7340308590816,
7.192872480681463, - 16.24367022206952],
[15.2, 99.12073082748223, - 223.9827649034903, 7.192872480658307,
- 16.24367022201719], [15.4, 100.5593053236117, - 227.2314989478887,
7.192872480636456, - 16.24367022196782],
[15.6, 101.9978798197369, - 230.4802329922776, 7.19287248061582,
- 16.24367022192119], [15.8, 103.4364543158581, - 233.7289670366574,
7.192872480596316, - 16.24367022187711],
[16.0, 104.8750288119755, - 236.9777010810286, 7.192872480577867,
- 16.24367022183542], [16.2, 106.3136033080893, - 240.2264351253917,
7.192872480560402, - 16.24367022179596],
[16.4, 107.7521778041997, - 243.4751691697471, 7.192872480543857,
- 16.24367022175857], [16.6, 109.1907523003069, - 246.7239032140952,
7.192872480528171, - 16.24367022172313],
[16.8, 110.6293267964111, - 249.9726372584365, 7.192872480513291,
- 16.24367022168951], [17.0, 112.0679012925123, - 253.2213713027712,
7.192872480499164, - 16.24367022165759],
[17.2, 113.5064757886108, - 256.4701053470996, 7.192872480485744,
- 16.24367022162727], [17.4, 114.9450502847066, - 259.7188393914221,
7.192872480472987, - 16.24367022159844],
[17.6, 116.3836247808, - 262.967573435739, 7.192872480460853,
- 16.24367022157103], [17.8, 117.822199276891, - 266.2163074800506,
7.192872480449304, - 16.24367022154493],
[18.0, 119.2607737729798, - 269.4650415243571, 7.192872480438305,
- 16.24367022152008], [18.2, 120.6993482690664, - 272.7137755686587,
7.192872480427823, - 16.2436702214964],
[18.4, 122.1379227651509, - 275.9625096129557, 7.19287248041783,
- 16.24367022147382], [18.6, 123.5764972612335, - 279.2112436572483,
7.192872480408296, - 16.24367022145228],
[18.8, 125.0150717573143, - 282.4599777015367, 7.192872480399196,
- 16.24367022143172], [19.0, 126.4536462533933, - 285.7087117458211,
7.192872480390505, - 16.24367022141208],
[19.2, 127.8922207494705, - 288.9574457901016, 7.1928724803822,
- 16.24367022139332], [19.4, 129.3307952455461, - 292.2061798343784,
7.192872480374261, - 16.24367022137538],
[19.6, 130.7693697416202, - 295.4549138786518, 7.192872480366667,
- 16.24367022135823], [19.8, 132.2079442376928, - 298.7036479229218,
7.1928724803594, - 16.24367022134181],
[20.0, 133.646518733764, - 301.9523819671886, 7.192872480352442,
- 16.24367022132608], [20.2, 135.0850932298338, - 305.2011160114523,
7.192872480345777, - 16.24367022131103],
[20.4, 136.5236677259023, - 308.449850055713, 7.19287248033939,
- 16.2436702212966], [20.6, 137.9622422219696, - 311.6985840999709,
7.192872480333267, - 16.24367022128276],
[20.8, 139.4008167180357, - 314.9473181442261, 7.192872480327393,
- 16.24367022126949], [21.0, 140.8393912141006, - 318.1960521884788,
7.192872480321758, - 16.24367022125676],
[21.2, 142.2779657101644, - 321.4447862327289, 7.192872480316347,
- 16.24367022124454], [21.4, 143.7165402062271, - 324.6935202769766,
7.192872480311151, - 16.2436702212328],
[21.6, 145.1551147022889, - 327.942254321222, 7.192872480306159,
- 16.24367022122152], [21.8, 146.5936891983496, - 331.1909883654652,
7.192872480301361, - 16.24367022121068],
[22.0, 148.0322636944094, - 334.4397224097063, 7.192872480296748,
- 16.24367022120025], [22.2, 149.4708381904683, - 337.6884564539453,
7.19287248029231, - 16.24367022119023],
[22.4, 150.9094126865263, - 340.9371904981824, 7.19287248028804,
- 16.24367022118058], [22.6, 152.3479871825835, - 344.1859245424176,
7.192872480283929, - 16.2436702211713],
[22.8, 153.7865616786399, - 347.4346585866509, 7.192872480279971,
- 16.24367022116235], [23.0, 155.2251361746955, - 350.6833926308825,
7.192872480276158, - 16.24367022115374],
[23.2, 156.6637106707504, - 353.9321266751124, 7.192872480272484,
- 16.24367022114544], [23.4, 158.1022851668045, - 357.1808607193407,
7.192872480268941, - 16.24367022113744],
[23.6, 159.540859662858, - 360.4295947635674, 7.192872480265526,
- 16.24367022112972], [23.8, 160.9794341589108, - 363.6783288077926,
7.192872480262232, - 16.24367022112228],
[24.0, 162.4180086549629, - 366.9270628520164, 7.192872480259053,
- 16.2436702211151], [24.2, 163.8565831510144, - 370.1757968962387,
7.192872480255986, - 16.24367022110817],
[24.4, 165.2951576470653, - 373.4245309404597, 7.192872480253024,
- 16.24367022110148], [24.6, 166.7337321431156, - 376.6732649846793,
7.192872480250163, - 16.24367022109501],
[24.8, 168.1723066391654, - 379.9219990288977, 7.192872480247399,
- 16.24367022108877], [25.0, 169.6108811352146, - 383.1707330731148,
7.192872480244728, - 16.24367022108274],
[25.2, 171.0494556312632, - 386.4194671173308, 7.192872480242146,
- 16.2436702210769], [25.4, 172.4880301273114, - 389.6682011615456,
7.192872480239649, - 16.24367022107127],
[25.6, 173.9266046233591, - 392.9169352057593, 7.192872480237234,
- 16.24367022106581], [25.8, 175.3651791194063, - 396.1656692499719,
7.192872480234898, - 16.24367022106054],
[26.0, 176.8037536154531, - 399.4144032941835, 7.192872480232638,
- 16.24367022105543], [26.2, 178.2423281114994, - 402.6631373383941,
7.19287248023045, - 16.24367022105049],
[26.4, 179.6809026075453, - 405.9118713826038, 7.19287248022833,
- 16.2436702210457], [26.6, 181.1194771035907, - 409.1606054268124,
7.192872480226279, - 16.24367022104107],
[26.8, 182.5580515996358, - 412.4093394710202, 7.192872480224291,
- 16.24367022103658], [27.0, 183.9966260956804, - 415.658073515227,
7.192872480222365, - 16.24367022103223]]
(%i11) xylist: makelist([points[i][2],points[i][3]],i,1,length(points));
(%o11) [[1, 0], [0.97994402898821, 0.15892333797882],
[0.9191251104626, 0.31115175589081], [0.81542552825771, 0.44864792902243],
[0.66479046167805, 0.55980839340965], [0.46013622929416, 0.62401577804146],
[0.18928641937503, 0.59157174929807], [- 0.14351602991004, 0.20333268046667],
[1.297647125294126, - 3.068808437402134],
[2.736235153012654, - 6.317573805762186],
[4.174812144974642, - 9.566313564697165],
[5.613387502220808, - 12.81504957243489],
[7.051962393128261, - 16.06378451492054],
[8.490537102310325, - 19.31251904332768],
[9.929111726293336, - 22.56125337790853],
[11.36768630509667, - 25.80998760981965],
[12.80626085773231, - 29.05872178231358],
[14.24483539417084, - 32.30745591805277],
[15.68340992004987, - 35.55619002984204],
[17.12198443875182, - 38.80492412535953],
[18.56055895240577, - 42.05365820943612],
[19.99913346240614, - 45.30239228523444],
[21.43770796969712, - 48.55112635489532],
[22.87628247493649, - 51.79986041990978],
[24.3148569785939, - 55.04859448134208],
[25.75343148101189, - 58.29732853996836],
[27.19200598244511, - 61.54606259636539],
[28.63058048308598, - 64.79479665096903],
[30.06915498308214, - 68.04353070411359],
[31.50772948254837, - 71.29226475605897],
[32.946303981575, - 74.54099880700967],
[34.3848784802339, - 77.78973285712839],
[35.82345297858284, - 81.03846690654586],
[37.26202747666867, - 84.28720095536814],
[38.70060197452971, - 87.53593500368193],
[40.13917647219756, - 90.78466905155874],
[41.57775096969843, - 94.03340309905791],
[43.01632546705426, - 97.28213714622905],
[44.45489996428349, - 100.5308711931139],
[45.89347446140172, - 103.7796052397477],
[47.33204895842222, - 107.0283392861605],
[48.77062345535633, - 110.2770733323779],
[50.2091979522138, - 113.5258073784221],
[51.64777244900304, - 116.774541424312],
[53.08634694573133, - 120.0232754700641],
[54.52492144240501, - 123.2720095156927],
[55.96349593902962, - 126.5207435612104],
[57.40207043561001, - 129.7694776066281],
[58.84064493215045, - 133.0182116519555],
[60.2792194286547, - 136.2669456972011],
[61.71779392512609, - 139.5156797423724],
[63.15636842156758, - 142.7644137874761],
[64.5949429179818, - 146.0131478325181],
[66.03351741437109, - 149.2618818775038],
[67.47209191073756, - 152.510615922438],
[68.9106664070831, - 155.7593499673248],
[70.3492409034094, - 159.0080840121681],
[71.78781539971797, - 162.2568180569714],
[73.2263898960102, - 165.5055521017377],
[74.66496439228735, - 168.7542861464699],
[76.10353888855052, - 172.0030201911705],
[77.54211338480074, - 175.2517542358419],
[78.98068788103896, - 178.5004882804861],
[80.41926237726602, - 181.7492223251052],
[81.85783687348271, - 184.9979563697008],
[83.29641136968974, - 188.2466904142745],
[84.73498586588774, - 191.4954244588278],
[86.17356036207731, - 194.7441585033622],
[87.61213485825901, - 197.9928925478787],
[89.05070935443335, - 201.2416265923786],
[90.48928385060079, - 204.4903606368629],
[91.92785834676174, - 207.7390946813325],
[93.36643284291661, - 210.9878287257884],
[94.80500733906577, - 214.2365627702314],
[96.24358183520955, - 217.4852968146622],
[97.68215633134828, - 220.7340308590816],
[99.12073082748223, - 223.9827649034903],
[100.5593053236117, - 227.2314989478887],
[101.9978798197369, - 230.4802329922776],
[103.4364543158581, - 233.7289670366574],
[104.8750288119755, - 236.9777010810286],
[106.3136033080893, - 240.2264351253917],
[107.7521778041997, - 243.4751691697471],
[109.1907523003069, - 246.7239032140952],
[110.6293267964111, - 249.9726372584365],
[112.0679012925123, - 253.2213713027712],
[113.5064757886108, - 256.4701053470996],
[114.9450502847066, - 259.7188393914221],
[116.3836247808, - 262.967573435739], [117.822199276891, - 266.2163074800506],
[119.2607737729798, - 269.4650415243571],
[120.6993482690664, - 272.7137755686587],
[122.1379227651509, - 275.9625096129557],
[123.5764972612335, - 279.2112436572483],
[125.0150717573143, - 282.4599777015367],
[126.4536462533933, - 285.7087117458211],
[127.8922207494705, - 288.9574457901016],
[129.3307952455461, - 292.2061798343784],
[130.7693697416202, - 295.4549138786518],
[132.2079442376928, - 298.7036479229218],
[133.646518733764, - 301.9523819671886],
[135.0850932298338, - 305.2011160114523],
[136.5236677259023, - 308.449850055713],
[137.9622422219696, - 311.6985840999709],
[139.4008167180357, - 314.9473181442261],
[140.8393912141006, - 318.1960521884788],
[142.2779657101644, - 321.4447862327289],
[143.7165402062271, - 324.6935202769766],
[145.1551147022889, - 327.942254321222],
[146.5936891983496, - 331.1909883654652],
[148.0322636944094, - 334.4397224097063],
[149.4708381904683, - 337.6884564539453],
[150.9094126865263, - 340.9371904981824],
[152.3479871825835, - 344.1859245424176],
[153.7865616786399, - 347.4346585866509],
[155.2251361746955, - 350.6833926308825],
[156.6637106707504, - 353.9321266751124],
[158.1022851668045, - 357.1808607193407],
[159.540859662858, - 360.4295947635674],
[160.9794341589108, - 363.6783288077926],
[162.4180086549629, - 366.9270628520164],
[163.8565831510144, - 370.1757968962387],
[165.2951576470653, - 373.4245309404597],
[166.7337321431156, - 376.6732649846793],
[168.1723066391654, - 379.9219990288977],
[169.6108811352146, - 383.1707330731148],
[171.0494556312632, - 386.4194671173308],
[172.4880301273114, - 389.6682011615456],
[173.9266046233591, - 392.9169352057593],
[175.3651791194063, - 396.1656692499719],
[176.8037536154531, - 399.4144032941835],
[178.2423281114994, - 402.6631373383941],
[179.6809026075453, - 405.9118713826038],
[181.1194771035907, - 409.1606054268124],
[182.5580515996358, - 412.4093394710202],
[183.9966260956804, - 415.658073515227]]
(%i12) plot2d([[discrete,xylist]],[x,-2,2],[y,-2,2]);
plot```
Run Example
```g:10;
(%o1)                                 10
(%i2) r0:rk([v,-g],[x,v],[0,10],[t,0,2,.1]),numer;
(%o2) [[0, 0, 10], [0.1, 0.95, 9.0], [0.2, 1.8, 8.0], [0.3, 2.55, 7.0],
[0.4, 3.2, 6.0], [0.5, 3.75, 5.0], [0.6, 4.2, 4.0], [0.7, 4.55, 3.0],
[0.8, 4.8, 2.0], [0.9, 4.95, 1.0], [1.0, 5.0, 0.0], [1.1, 4.95, - 1.0],
[1.2, 4.8, - 2.0], [1.3, 4.55, - 3.0], [1.4, 4.2, - 4.0], [1.5, 3.75, - 5.0],
[1.6, 3.2, - 6.0], [1.7, 2.55, - 7.0], [1.8, 1.8, - 8.0], [1.9, 0.95, - 9.0],
[2.0, 2.2204460492503131E-16, - 10.0]]
(%i3) last(r0);
(%o3)                [2.0, 2.2204460492503131E-16, - 10.0]
(%i4) ```
Run Example
```gpot: 2;
(%o1)                                  2
(%i2) dxdt: vx;
(%o2)                                 vx
(%i3) dvxdt: -x/(x^2+y^2)^((gpot+1)/2);
x
(%o3)                           - ------------
2    2 3/2
(y  + x )
(%i4) dydt: vy;
(%o4)                                 vy
(%i5) dvydt: -y/(x^2+y^2)^((gpot+1)/2);
y
(%o5)                           - ------------
2    2 3/2
(y  + x )
(%i6) x0: 1;
(%o6)                                  1
(%i7) y0: 0;
(%o7)                                  0
(%i8) vx0: 0;
(%o8)                                  0
(%i9) vy0: 0.8;
(%o9)                                 0.8
(%i10) points: rk([dxdt,dydt,dvxdt,dvydt],[x,y,vx,vy],[x0,y0,vx0,vy0],[t,0,7,0.2]);
(%o10) [[0, 1, 0, 0, 0.8], [0.2, 0.97999421704924, 0.15892742751229,
- 0.2001025160355, 0.78387982670285], [0.4, 0.91992477539928,
0.31130883042266, - 0.40069103567061, 0.73403855129627],
[0.6, 0.81969797290704, 0.4499869300834, - 0.6015349792668, 0.64574431142578],
[0.8, 0.67943194816545, 0.56646157823908, - 0.80046211237816,
0.51008205923802], [1.0, 0.50007609340413, 0.64989772975182,
- 0.99067437818579, 0.31226852927509],
[1.2, 0.28488206581699, 0.68573619492816, - 1.154350597572916,
0.029522800367278], [1.4, 0.042928014491224, 0.65404654156545,
- 1.247288109832067, - 0.3682153685148],
[1.6, - 0.20271235710731, 0.52952065968921, - 1.167254063519093,
- 0.89707392610171], [1.8, - 0.40031871269041, 0.29227121987378,
- 0.73648713774529, - 1.460093684408463],
[2.0, - 0.46914445310449, - 0.032237668042007, 0.089008666058971,
- 1.697401918745894], [2.2, - 0.36872520390875, - 0.34545228642875,
0.86057497922282, - 1.359149390883167],
[2.4, - 0.15472722112283, - 0.55952273659485, 1.211388325151852,
- 0.77745928398491], [2.6, 0.094441775637197, - 0.66165362760751,
1.24404023735459, - 0.26604396661924],
[2.8, 0.33307849962476, - 0.67496920631646, 1.127190352667443,
0.11154420498625], [3.0, 0.5413930776246, - 0.62442259088353,
0.95021535803548, 0.37796396019608], [3.2, 0.71171796855138,
- 0.52919740458867, 0.75110702028402, 0.56268851871172],
[3.4, 0.84138142158048, - 0.40334713184739, 0.54507390482585,
0.68708864750984], [3.6, 0.92966528947895, - 0.25746355290309,
0.33780835577458, 0.76477331609707], [3.8, 0.97653394486419,
- 0.10001330056676, 0.13101118995405, 0.80371289808091],
[4.0, 0.98210324973996, 0.061701016441757, - 0.075250199798659,
0.8077685797455], [4.2, 0.9464389189863, 0.22080769085873, - 0.28140491836564,
0.77745976599667], [4.4, 0.86953599418275, 0.37021897328556,
- 0.48760340337611, 0.71007275523868],
[4.600000000000001, 0.75146261570436, 0.50194296737974, - 0.69275988893121,
0.59913418497722], [4.800000000000001, 0.59276766071119, 0.60622052730332,
- 0.89271548462831, 0.43316951822794],
[5.0, 0.39545391231512, 0.67033984079283, - 1.07605754862535,
0.19376207876003], [5.2, 0.16528433080244, 0.67707076294238,
- 1.214117386895035, - 0.14582671555121],
[5.4, - 0.082768044345798, 0.60342045443836, - 1.238187281398755,
- 0.61339049099164], [5.600000000000001, - 0.31294748285777, 0.42420713853014,
- 1.004893830144142, - 1.187241593786015],
[5.800000000000001, - 0.45572588873763, 0.13576834190163, - 0.35294052232715,
- 1.644794132191851], [6.0, - 0.4378436229968, - 0.19698631384732,
0.52249964033598, - 1.584629237694605],
[6.2, - 0.26873279444383, - 0.46569783444521, 1.09519516733302,
- 1.064764544269772], [6.4, - 0.027727355703475, - 0.61993828116744,
1.261939641583499, - 0.49229947528373],
[6.600000000000001, 0.22090409860826, - 0.67113605730431, 1.20013891355373,
- 0.043155787413877], [6.800000000000001, 0.44593184767591,
- 0.64574581962993, 1.040531929542131, 0.27804338280109],
[7.0, 0.6346549518856, - 0.56640000569976, 0.84323841366651, 0.50151890490124]]
(%i11) xylist: makelist([points[i][2],points[i][3]],i,1,length(points));
(%o11) [[1, 0], [0.97999421704924, 0.15892742751229],
[0.91992477539928, 0.31130883042266], [0.81969797290704, 0.4499869300834],
[0.67943194816545, 0.56646157823908], [0.50007609340413, 0.64989772975182],
[0.28488206581699, 0.68573619492816], [0.042928014491224, 0.65404654156545],
[- 0.20271235710731, 0.52952065968921],
[- 0.40031871269041, 0.29227121987378],
[- 0.46914445310449, - 0.032237668042007],
[- 0.36872520390875, - 0.34545228642875],
[- 0.15472722112283, - 0.55952273659485],
[0.094441775637197, - 0.66165362760751],
[0.33307849962476, - 0.67496920631646], [0.5413930776246, - 0.62442259088353],
[0.71171796855138, - 0.52919740458867],
[0.84138142158048, - 0.40334713184739],
[0.92966528947895, - 0.25746355290309],
[0.97653394486419, - 0.10001330056676], [0.98210324973996, 0.061701016441757],
[0.9464389189863, 0.22080769085873], [0.86953599418275, 0.37021897328556],
[0.75146261570436, 0.50194296737974], [0.59276766071119, 0.60622052730332],
[0.39545391231512, 0.67033984079283], [0.16528433080244, 0.67707076294238],
[- 0.082768044345798, 0.60342045443836],
[- 0.31294748285777, 0.42420713853014],
[- 0.45572588873763, 0.13576834190163],
[- 0.4378436229968, - 0.19698631384732],
[- 0.26873279444383, - 0.46569783444521],
[- 0.027727355703475, - 0.61993828116744],
[0.22090409860826, - 0.67113605730431],
[0.44593184767591, - 0.64574581962993], [0.6346549518856, - 0.56640000569976]]
(%i12) plot2d([[discrete,xylist]],[x,-2,2],[y,-2,2]);
plot```

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