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desolve

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(%i1)eq1:'diff(ta(t),t)=(1/c)*[f(t)-(l+g)*ta(t)+g*tao(t)];
                d             g tao(t) - (l + g) ta(t) + f(t)
(%o1)           -- (ta(t)) = [-------------------------------]
                dt                           c
(%i2) eq2:'diff(tao(t),t)=(1/co)*(g*ta(t)-g*tao(t));
                       d             g ta(t) - g tao(t)
(%o2)                  -- (tao(t)) = ------------------
                       dt                    co
(%i3) desolve([eq1,eq2],[ta(t),tao(t)]);
(%o3) [ta(t) = 
             g tao(t) - (l + g) ta(t) + f(t)
    laplace([-------------------------------], t, g33270) + ta(0)
                            c
ilt(-------------------------------------------------------------, g33270, t), 
                               g33270
                                            g tao(t) - (l + g) ta(t) + f(t)
tao(t) = ilt((tao(0) co g33270 + g laplace([-------------------------------], 
                                                           c
                                2
t, g33270) + ta(0) g)/(co g33270  + g g33270), g33270, t)]
(%i4) 
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
eqn : ’diff(t(t),t) = (t-y(t))/2;
                                           t - y(t)
(%o1)                      diff(t(t), t) = --------
                                              2
(%i2) atvalue ( y(t), t=0, 1);
(%o2)                                  1
(%i3) gsoln : desolve(eqn,y(t));
                                                             2
                   2 laplace(diff(t(t), t), t, g33270) g33270  - 1
(%o3) y(t) = ilt(- -----------------------------------------------, g33270, t)
                                             2
                                       g33270
(%i4) 

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