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ic2

Run Example
(%i1)eq : 'diff(y,x,2) + 6*'diff(y,x) + 9*y = 4*exp(-x);
                           2
                          d y     dy             - x
(%o1)                     --- + 6 -- + 9 y = 4 %e
                            2     dx
                          dx
(%i2) sol1 : ode2(eq,y,x);
                             - x                   - 3 x
(%o2)                  y = %e    + (%k2 x + %k1) %e
(%i3)  y : ic2(sol1,x=0,y=2,'diff(y,x)=-2);
                               - x               - 3 x
(%o3)                    y = %e    + (2 x + 1) %e
(%i4) plot2d(exp(-x)+ (-4*x-1)*exp(-3*x),[x,-1,1]);
plotplot2d(exp(-x)+ (-4*x-1)*exp(-3*x),[x,-1,1]);
Run Example
eq1:'diff(y,x,2)+'diff(y,x)-sqrt(2)*sin(sqrt(2)*x);
                        2
                       d y   dy
(%o1)                  --- + -- - sqrt(2) sin(sqrt(2) x)
                         2   dx
                       dx
(%i2) sol2:ode2(eq1,y,x);
              sqrt(2) sin(sqrt(2) x) + cos(sqrt(2) x)         - x
(%o2)   y = - --------------------------------------- + %k2 %e    + %k1
                                 3
(%i3) ic2(sol2, x=0, y=10, 'diff(y, x)=0);
                                                             - x
               sqrt(2) sin(sqrt(2) x) + cos(sqrt(2) x)   2 %e
(%o3)    y = - --------------------------------------- - ------- + 11
                                  3                         3
(%i4) expand(%);
(%o4)             
Run Example
eqn: 'diff(y,x,2)-3*'diff(y,x)+2*y=x^2;
                              2
                             d y     dy          2
(%o1)                        --- - 3 -- + 2 y = x
                               2     dx
                             dx
(%i2) sol: ode2(eqn,y,x);
                                                2
                             2 x         x   2 x  + 6 x + 7
(%o2)              y = %k1 %e    + %k2 %e  + --------------
                                                   4
(%i3) ic2(sol,x=-1,y=-2,'diff(y,x)=2);
                          2 x + 2                  2
                     17 %e              x + 1   2 x  + 6 x + 7
(%o3)            y = ------------ - 7 %e      + --------------
                          4                           4
(%i4) 

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Help for Ic2