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rk

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

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rk-sin

result:rk((y-x)*sin(y...

Calculate

rk-sin

sol:rk([-(-2+(1/x))*y...

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rk

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

Calculate

rk-sin

sol:rk([-(-2+(1/x))*y...

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rk

g:10;

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

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rk-sin

result: rk(x*sin(y)+y...

Calculate

rk-sin

rk(x-sin(y),y,1,[x,0,...

Calculate

rk-sin

result: rk(x*sin(y)+y...

Calculate

rk-sin

result: rk(x*sin(y)+y...

Calculate

rk

Run Example
(%i1)result: rk(((y-x)*sin(y*x)),y,5,[x,-3,10,0.1]);
(%o1) [[- 3, 5], [- 2.9, 4.437674780748283], [- 2.8, 4.462011491837269], 
[- 2.7, 4.586110203555572], [- 2.6, 4.745473012471332], 
[- 2.5, 4.925332389376685], [- 2.4, 5.122082648452681], 
[- 2.3, 5.335951371507967], [- 2.2, 5.568610493939755], 
[- 2.1, 5.822456451362866], [- 2.0, 6.100459972766338], 
[- 1.9, 6.406213064540006], [- 1.8, 6.744061436492595], 
[- 1.7, 7.119298743148908], [- 1.6, 7.538429709865417], 
[- 1.5, 8.009523349402457], [- 1.4, 8.542688101917909], 
[- 1.3, 9.150710292947638], [- 1.2, 9.849899831501928], 
[- 1.1, 10.66115567573268], [- 1.0, 11.61109694091529], 
[- 0.9, 12.73240422801607], [- 0.8, 14.05951126915607], 
[- 0.7, 15.60109155789042], [- 0.6, 17.18216614036799], 
[- 0.5, 17.60870376473243], [- 0.4, 16.28352186031173], 
[- 0.3, 17.04699895963675], [- 0.2, 18.67153483455791], 
[- 0.1, 18.15796170018035], [0.0, 16.9748108649895], [0.1, 18.14294259758864], 
[0.2, 18.65870130500707], [0.3, 17.07863293942715], [0.4, 16.36161915486202], 
[0.5, 17.5932586257231], [0.6, 17.20638305440314], [0.7, 15.72355470091753], 
[0.8, 14.35441214611837], [0.9, 13.42256966861004], [1.0, 13.52032027380415], 
[1.100000000000001, 14.3288684722572], [1.2, 13.72473312553487], 
[1.3, 12.80555990210402], [1.4, 11.90681687799816], [1.5, 11.09223904103386], 
[1.600000000000001, 10.37048718816664], [1.7, 9.73431228120943], 
[1.800000000000001, 9.172280847344435], [1.9, 8.673144986813446], 
[2.0, 8.227216440159339], [2.100000000000001, 7.826528688339948], 
[2.2, 7.464611553660763], [2.300000000000001, 7.136202249626115], 
[2.4, 6.836992826002452], [2.5, 6.56343176529668], 
[2.600000000000001, 6.312573458231622], [2.7, 6.081965187768359], 
[2.800000000000001, 5.869562710006372], [2.9, 5.673667912758386], 
[3.0, 5.492884151874554], [3.100000000000001, 5.326086544875647], 
[3.2, 5.172405815628657], [3.300000000000001, 5.031225281935476], 
[3.4, 4.902191139052023], [3.5, 4.785235807979614], 
[3.600000000000001, 4.680611441356332], [3.7, 4.588922683021562], 
[3.800000000000001, 4.51112867183104], [3.9, 4.448446165404911], 
[4.0, 4.402028625374295], [4.100000000000001, 4.372264036926429], 
[4.2, 4.357670552299489], [4.300000000000001, 4.353848144745031], 
[4.4, 4.35352274131246], [4.5, 4.348398947084699], 
[4.600000000000001, 4.331881719075291], [4.7, 4.30058442074811], 
[4.800000000000001, 4.253713345264512], [4.9, 4.191273181948321], 
[5.0, 4.112365821617212], [5.1, 4.014475991336682], 
[5.200000000000001, 3.895535531390356], [5.300000000000001, 3.76140438672922], 
[5.4, 3.63102586278815], [5.5, 3.521490474569624], [5.6, 3.433539532480061], 
[5.700000000000001, 3.359750969330649], 
[5.800000000000001, 3.293981305095513], [5.9, 3.232971397896864], 
[6.0, 3.175243192424779], [6.1, 3.120124170456137], 
[6.200000000000001, 3.06726322035541], [6.300000000000001, 3.016437700796482], 
[6.4, 2.967483558543225], [6.5, 2.920270016164411], 
[6.600000000000001, 2.874690047640952], [6.700000000000001, 2.83065785565719], 
[6.800000000000001, 2.788112373522923], [6.9, 2.747031495963191], 
[7.0, 2.707473456048027], [7.100000000000001, 2.669698542533514], 
[7.200000000000001, 2.63455558731323], [7.300000000000001, 2.604793641130309], 
[7.4, 2.588491059751161], [7.5, 2.573654276997369], 
[7.600000000000001, 2.492493336680742], 
[7.700000000000001, 2.474084174762838], 
[7.800000000000001, 2.481051681661025], [7.9, 2.310377109352376], 
[8.0, 2.470859971844421], [8.100000000000001, 2.52069928797462], 
[8.200000000000001, 2.421350083412636], 
[8.300000000000001, 2.405530821339541], [8.4, 2.474603317024763], 
[8.5, 2.327575490467552], [8.600000000000001, 2.472005075935695], 
[8.700000000000001, 2.194765551000867], 
[8.800000000000001, 1.918719343219902], [8.9, 1.750627588397179], 
[9.0, 1.357622827504271], [9.100000000000001, 1.138644402246663], 
[9.200000000000001, 0.74957332797638], [9.300000000000001, 1.106580498354709], 
[9.4, 0.66273073002655], [9.5, 0.82883942730555], 
[9.600000000000001, 1.038800906615676], 
[9.700000000000001, 1.583050215238806], 
[9.800000000000001, 1.641985526668064], [9.9, 1.778801529616948], 
[10.0, 1.752012636075708]]
(%i2) plot2d([discrete, result]);
plotplot2d([discrete, result]);
Run Example
b:1.4;
(%o1)                                 1.4
(%i2) f:integrate(x^3+b*x,x);
                                   4
                                  x         2
(%o2)                             -- + 0.7 x
                                  4
(%i3) c:[[0,0,1],[1,0,1]];
(%o3)                       [[0, 0, 1], [1, 0, 1]]
(%i4) d:[[0,-1,1],[1,-1,1]];
(%o4)                     [[0, - 1, 1], [1, - 1, 1]]
(%i5) e:[[1,0],[2,2],[1,4]];
(%o5)                      [[1, 0], [2, 2], [1, 4]]
(%i6) c+d;
(%o6)                     [[0, - 1, 2], [2, - 1, 2]]
(%i7) g:rk(x*t^2+1,x,1,[t,0,5,0.05]);
(%o7) [[0, 1], [0.05, 1.050043230000824], [0.1, 1.100358392302506], 
[0.15, 1.151252256251517], [0.2, 1.203070682271946], 
[0.25, 1.256200664975782], [0.3, 1.311073451991812], 
[0.35, 1.368168918043225], [0.4, 1.428021402924487], [0.45, 1.49122726270502], 
[0.5, 1.558454438309783], [0.55, 1.630454417935699], [0.6, 1.708077063930385], 
[0.65, 1.792288896556607], [0.7, 1.884195584148339], 
[0.75, 1.985069591726813], [0.8, 2.096384201806075], 
[0.85, 2.219855460129051], [0.9, 2.357494039985001], 
[0.95, 2.511669594713375], [1.0, 2.68519092394427], [1.05, 2.881406276293514], 
[1.1, 3.104329433446791], [1.15, 3.358798983182146], [1.2, 3.650680551476201], 
[1.25, 3.987124948419813], [1.3, 4.376899499845258], 
[1.35, 4.830815723484105], [1.4, 5.362284584075836], 
[1.45, 5.988041707907986], [1.5, 6.729100417981714], 
[1.55, 7.612012090598515], [1.6, 8.670543782546819], 
[1.65, 9.947926210682667], [1.7, 11.49988668986295], 
[1.75, 13.39877001591107], [1.8, 15.7391781643573], [1.85, 18.64574609853908], 
[1.9, 22.28394481249247], [1.95, 26.87520810322936], [2.0, 32.71828446293331], 
[2.05, 40.2196255133936], [2.1, 49.9370029880612], [2.15, 62.6426587060535], 
[2.2, 79.41555266386095], [2.25, 101.7773527301092], [2.3, 131.8947915630653], 
[2.35, 172.8836808122158], [2.4, 229.2701596124872], 
[2.45, 307.6975718002058], [2.5, 418.0209883947317], [2.55, 575.019909775361], 
[2.6, 801.1073419305448], [2.65, 1130.662405450248], [2.7, 1617.038014323403], 
[2.75, 2344.02665681902], [2.8, 3444.8426124063], [2.85, 5133.928302505407], 
[2.9, 7760.907189093824], [2.95, 11903.25837766975], [3.0, 18527.55306182536], 
[3.05, 29273.66115194422], [3.1, 46962.42666137379], 
[3.15, 76514.91360128063], [3.2, 126640.0625174378], 
[3.25, 212977.0550346421], [3.3, 364030.8885892539], 
[3.35, 632549.0802504189], [3.4, 1117654.217478409], 
[3.45, 2008558.083224253], [3.5, 3672241.833212971], 
[3.55, 6832098.316909418], [3.6, 1.2937747095597789E+7], 
[3.65, 2.4943099406644337E+7], [3.7, 4.8970506523727402E+7], 
[3.75, 9.7930077100773603E+7], [3.8, 1.9952600002271998E+8], 
[3.85, 4.1427528675176996E+8], [3.9, 8.7677579237233639E+8], 
[3.95, 1.891914647679625E+9], [4.0, 4.1632362009537621E+9], 
[4.05, 9.3450085741359539E+9], [4.100000000000001, 2.1401768106080246E+10], 
[4.15, 5.0019871071178444E+10], [4.2, 1.193327361799743E+11], 
[4.25, 2.9067076789243634E+11], [4.3, 7.230492662165752E+11], 
[4.350000000000001, 1.8372093313144292E+12], [4.4, 4.7694954835370332E+12], 
[4.45, 1.2653406535669316E+13], [4.5, 3.431319792256277E+13], 
[4.55, 9.5132832614838766E+13], [4.600000000000001, 2.6971879270752525E+14], 
[4.65, 7.8216577997292675E+14], [4.7, 2.320532870293689E+15], 
[4.75, 7.044847612692134E+15], [4.800000000000001, 2.1889873375913464E+16], 
[4.850000000000001, 6.9629708917940152E+16], [4.9, 2.2678618596218451E+17], 
[4.95, 7.5648332991151309E+17], [5.0, 2.5848298673295032E+18]]
(%i8) plot2d([discrete,g]);
plotplot2d([discrete,g]);
Run Example
result: rk(x*sin(y)+y*sin(x),y,-2,[x,-1,5,0.1]);
(%o1) [[- 1, - 2], [- 0.9, - 1.757037313842795], [- 0.8, - 1.548459932584421], 
[- 0.7, - 1.374516940537385], [- 0.6, - 1.233077439694283], 
[- 0.5, - 1.120873797280061], [- 0.4, - 1.034424889817311], 
[- 0.3, - 0.97058527266901], [- 0.2, - 0.92681481010586], 
[- 0.1, - 0.90128300774374], [0.0, - 0.89289380364406], 
[0.1, - 0.90128300752101], [0.2, - 0.9268148080466], 
[0.3, - 0.97058526654018], [0.4, - 1.034424879109829], 
[0.5, - 1.120873786954176], [0.6, - 1.2330774433845], 
[0.7, - 1.374516976857475], [0.8, - 1.548460005089033], 
[0.9, - 1.757037378545495], [1.0, - 1.999999966332647], 
[1.1, - 2.273542834416308], [1.2, - 2.569945307139254], 
[1.3, - 2.878686109637773], [1.4, - 3.188834454277601], 
[1.5, - 3.491528583997136], [1.6, - 3.781340608092715], 
[1.7, - 4.056277042668273], [1.8, - 4.316991168281269], 
[1.9, - 4.565893500557055], [2.0, - 4.806544609723964], 
[2.1, - 5.043434142234045], [2.2, - 5.282129056006286], 
[2.3, - 5.529755507529757], [2.4, - 5.795752106236415], 
[2.5, - 6.092620793642309], [2.6, - 6.435618295364179], 
[2.7, - 6.838407169807223], [2.8, - 7.299883577223483], 
[2.9, - 7.785021287060351], [3.0, - 8.226030541742771], 
[3.100000000000001, - 8.561183104399884], [3.2, - 8.767796222021325], 
[3.3, - 8.856648314711979], [3.4, - 8.852334311213076], 
[3.5, - 8.780578101503691], [3.600000000000001, - 8.662920262388715], 
[3.7, - 8.515099479161721], [3.800000000000001, - 8.347124125794425], 
[3.9, - 8.164016944162988], [4.0, - 7.966528027506175], 
[4.100000000000001, - 7.751277528788695], [4.2, - 7.509800462421755], 
[4.300000000000001, - 7.225635752603592], [4.4, - 6.867847190522696], 
[4.5, - 6.379870783378075], [4.600000000000001, - 5.680097831240163], 
[4.7, - 4.768964238327176], [4.800000000000001, - 3.912307601930725], 
[4.9, - 3.343828579725686], [5.0, - 3.024003391891168]]
(%i2) 

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