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atvalue-bc2-diff-ode2-plot2d-rhs
 plot2d(rhs(sol1),[x,1,3]);

eqn: 'diff(y,x,2)-3*'...

atvalue(y(x),x=1,-2);

atvalue(y(x),x=3,0);

Calculate

atvalue-diff

ode: 'diff(w(x), t, 4...

atvalue('diff(w(x), x...

atvalue('diff(w(x), x...

Calculate

atvalue-desolve-diff-expand

eqn: 'diff(vo(t), t) ...

atvalue(vo(t), t=0, 0);

gsol: desolve(eqn, vo...

Calculate

atvalue-diff-laplace-solve

unitstep(x):= if x<...

ode: 'diff(y(t), t, 2...

atvalue(y(t), t=0, 0);

Calculate

atvalue-cos-desolve-diff-integrate-pi-ratsimp

eq: diff(y(x),x)-x*y(...

atvalue(y(x),x=0,1);

atvalue(diff(y(x),x),...

Calculate

atvalue-depends-diff-integrate-log-plot3d-solve
plot3d(

k1(temp);

k2(Temp);

log(k1)=7.176-(3.85/T...

Calculate

atvalue-diff-printprops

atvalue (f(x,y), [x =...

atvalue ('diff (f(x,...

printprops (all, atv...

Calculate

atvalue-diff-ode2-plot3d
plot3d(

k1:10^(7.176-(3.85/Te...

k2:10^(9.942-(4.05/Te...

OH=10^(pH-14);

Calculate

atvalue-diff-ode2

eqn: diff(y(x),x,2)-3...

atvalue(y(x),x=1,-2);

atvalue(y(x),x=3,0);

Calculate

atvalue-diff-exp-ode2-plot3d
plot3d(

k1:exp(7.176-(3.85/Te...

k2:exp(9.942-(4.05/Te...

OH:10^(pH-14);

Calculate

atvalue

Run Example
(%i1)assume(V>
0, R>
0, L>
0, C>
0);
(%o1)                    [V > 0, R > 0, L > 0, C > 0]
(%i2) assume(C*R^2 - 4*L >
 0);
                                     2
(%o2)                            [C R  > 4 L]
(%i3) ec  : R*x(t) + L*diff(x(t),t) + integrate(x(t), t)/C = V;
                                             /
                                             [
                                             I x(t) dt
                                             ]
                              d              /
(%o3)               x(t) R + (-- (x(t))) L + --------- = V
                              dt                 C
(%i4) ecd : diff(ec, t);
                                     2
                    d               d               x(t)
(%o4)              (-- (x(t))) R + (--- (x(t))) L + ---- = 0
                    dt                2              C
                                    dt
(%i5) e2:laplace(ecd,t,s);
                                                     !
                                            d        !
(%o5) (s laplace(x(t), t, s) - x(0)) R + (- -- (x(t))!
                                            dt       !
                                                     !t = 0
                    2                                   laplace(x(t), t, s)
                 + s  laplace(x(t), t, s) - x(0) s) L + ------------------- = 0
                                                                 C
(%i6) atvalue( x(t), t=0, 0);
(%o6)                                  0
(%i7) atvalue( diff(x(t), t), t=0, V/L);
                                       V
(%o7)                                  -
                                       L
(%i8) e4:solve(e2,laplace(x(t),t,s));
                                                   !
                                          d        !
                              x(0) C R + (-- (x(t))!      + x(0) s) C L
                                          dt       !
                                                   !t = 0
(%o8)  [laplace(x(t), t, s) = -----------------------------------------]
                                                  2
                                         s C R + s  C L + 1
(%i9) ilt(e2,s,t);
(%o9) ilt((s laplace(x(t), t, s) - x(0)) R, s, t)
                   !
          d        !         2
 + ilt((- -- (x(t))!      + s  laplace(x(t), t, s) - x(0) s) L, s, t)
          dt       !
                   !t = 0
       laplace(x(t), t, s)
 + ilt(-------------------, s, t) = 0
                C
(%i10) 
Run Example
gpot: 2;
(%o1)                                  2
(%i2) r: sqrt(x(t)^2 +y(t)^2);
                                    2       2
(%o2)                         sqrt(y (t) + x (t))
(%i3) r_potf: r^-(gpot+1);
                                      1
(%o3)                         ------------------
                                2       2    3/2
                              (y (t) + x (t))
(%i4) dgl_xt: 'diff(x(t),t,2)=-x(t)*r_potf;
                        2
                       d                     x(t)
(%o4)                  --- (x(t)) = - ------------------
                         2              2       2    3/2
                       dt             (y (t) + x (t))
(%i5) dgl_yt: 'diff(y(t),t,2)=-y(t)*r_potf;
                        2
                       d                     y(t)
(%o5)                  --- (y(t)) = - ------------------
                         2              2       2    3/2
                       dt             (y (t) + x (t))
(%i6) atvalue(x(t),t=0,1);
(%o6)                                  1
(%i7) atvalue(y(t),t=0,0);
(%o7)                                  0
(%i8) atvalue('diff(x(t),t),t=0,0);
(%o8)                                  0
(%i9) atvalue('diff(y(t),t),t=0,1);
(%o9)                                  1
(%i10) desolve([dgl_xt,dgl_yt],[x(t),y(t)]);
                                           x(t)
                   g33270 - laplace(------------------, t, g33270)
                                      2       2    3/2
                                    (y (t) + x (t))
(%o10) [x(t) = ilt(-----------------------------------------------, g33270, 
                                             2
                                       g33270
                                       y(t)
                        laplace(------------------, t, g33270) - 1
                                  2       2    3/2
                                (y (t) + x (t))
       t), y(t) = ilt(- ------------------------------------------, g33270, t)]
                                               2
                                         g33270
(%i11) 
Run Example
Gc:0;
(%o1)                                  0
(%i2)  Rg:0;
(%o2)                                  0
(%i3)  Ro1:0;
(%o3)                                  0
(%i4)  Ro2:0;
(%o4)                                  0
(%i5) v(t):=0;
(%o5)                              v(t) := 0
(%i6) i(t):=IL;
(%o6)                             i(t) := IL
(%i7) atvalue(vc(t), t=0, VG);
(%o7)                                 VG
(%i8) atvalue(ig(t), t=0, IL);
(%o8)                                 IL
(%i9) atvalue(i1(t), t=0, IL);
(%o9)                                 IL
(%i10) atvalue(i2(t), t=0, 0);
(%o10)                                 0
(%i11) atvalue(vut1(t), t=0, 0);
(%o11)                                 0
(%i12) atvalue(iut1(t), t=0, 0);
(%o12)                                 0
(%i13) vFW1(t):=-VG;
(%o13)                          vFW1(t) := - VG
(%i14) iFW1(t):=0;
(%o14)                           iFW1(t) := 0
(%i15) vFW2(t):=0;
(%o15)                           vFW2(t) := 0
(%i16) atvalue(vut2(t), t=0, 0);
(%o16)                                 0
(%i17) eqi1:laplace(ig(t) = Gc*vc(t) + C*'diff(vc(t),t,1) + i(t),t,s);
                                                                   IL
(%o17)    laplace(ig(t), t, s) = C (s laplace(vc(t), t, s) - VG) + --
                                                                   s
(%i18) eqi2:laplace(i(t) + iFW1(t) = i1(t),t,s);
                           IL
(%o18)                     -- = laplace(i1(t), t, s)
                           s
(%i19) eqi3:laplace(Gc*vc(t) + C*'diff(vc(t),t,1) + iut1(t) = iFW1(t),t,s);
(%o19)   C (s laplace(vc(t), t, s) - VG) + laplace(iut1(t), t, s) = 0
(%i20) eqv1:laplace(VG = Rg*ig(t) + v(t) + Ro1*i1(t) + Lo1*'diff(i1(t),t,1) + Lu*'diff(i2(t),t,1),t,s);
       VG
(%o20) -- = Lo1 (s laplace(i1(t), t, s) - IL) + Lu s laplace(i2(t), t, s)
       s
(%i21) eqv2:laplace(vut1(t) = vFW1(t) + Ro1*i1(t) + Lo1*'diff(i1(t),t,1) + Lu*'diff(i2(t),t,1),t,s);
                                  VG
(%o21) laplace(vut1(t), t, s) = - -- + Lo1 (s laplace(i1(t), t, s) - IL)
                                  s
                                                    + Lu s laplace(i2(t), t, s)
(%i22) eqv3:laplace(v(t) = vc(t) + vFW1(t),t,s);
                                                    VG
(%o22)                   0 = laplace(vc(t), t, s) - --
                                                    s
(%i23) eqv4:laplace(vut2(t) = vFW2(t) + Ro2*i2(t) + Lo2*'diff(i2(t),t,1) + Lu*'diff(i1(t),t,1),t,s);
(%o23) laplace(vut2(t), t, s) = Lu (s laplace(i1(t), t, s) - IL)
                                                   + Lo2 s laplace(i2(t), t, s)
(%i24) sol:solve([	eqi1,	eqi2,	eqi3,	eqv1,	eqv2,	eqv3,	eqv4],[	'laplace(vc(t),t,s),	'laplace(ig(t),t,s),	'laplace(i1(t),t,s),	'laplace(iFW1(t),t,s),	'laplace(i2(t),t,s),	'laplace(vut2(t),t,s),	'laplace(vFW1(t),t,s)]);
(%o24)                                []
(%i25) 
[assume,atvalue,desolve,diff] [assume,atvalue,diff,exp,laplace] [assume,atvalue,diff,exp] [assume,atvalue,diff,ilt,laplace,limit,solve] [assume,atvalue,diff,ilt,laplace,solve] [assume,atvalue,diff,laplace,limit,solve] [assume,atvalue,diff,laplace,solve] [assume,atvalue,diff,ode2] [atvalue,bc2,desolve,diff,ode2,ratsimp] [atvalue,bc2,diff,ode2,plot2d,rhs] [atvalue,cos,desolve,diff,integrate,pi,ratsimp] [atvalue,cos,desolve,diff,sin] [atvalue,cos,desolve,diff] [atvalue,delta,diff,ilt,lambda,laplace,map,solve] [atvalue,delta,diff,ilt,solve] [atvalue,depends,diff,integrate,log,plot3d,solve] [atvalue,depends,diff,integrate,log,plot3d] [atvalue,depends,diff,log,ode2,plot3d] [atvalue,desolve,diff,ev,rhs] [atvalue,desolve,diff,exp,ilt,plot2d] [atvalue,desolve,diff,exp,integrate,plot2d] [atvalue,desolve,diff,exp,plot2d] [atvalue,desolve,diff,exp] [atvalue,desolve,diff,expand] [atvalue,desolve,diff,ilt] [atvalue,desolve,diff,log] [atvalue,desolve,diff,ratsimp] [atvalue,desolve,diff,rhs] [atvalue,desolve,diff,sin] [atvalue,desolve,diff] [atvalue,desolve] [atvalue,diff,ev,ilt,laplace,solve] [atvalue,diff,exp,integrate,plot3d,solve] [atvalue,diff,exp,ode2,plot3d] [atvalue,diff,exp] [atvalue,diff,ilt,lambda,laplace,map,ratsimp,solve] [atvalue,diff,ilt,lambda,laplace,map,solve] [atvalue,diff,ilt,laplace,solve] [atvalue,diff,ilt,laplace] [atvalue,diff,laplace,solve] [atvalue,diff,laplace] [atvalue,diff,log,ode2,plot3d,solve] [atvalue,diff,log,ode2,plot3d] [atvalue,diff,ode2,plot3d,solve] [atvalue,diff,ode2,plot3d] [atvalue,diff,ode2] [atvalue,diff,plot3d] [atvalue,diff,solve] [atvalue,diff] [atvalue]

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