ODEs
Solutions
Following is the MAPLE sequence of steps to solve Example 1
> Example 1:#a]
> deq:=diff(y(x),x$3)-3*diff(y(x),x$2)-4*diff(y(x),x)+12*y(x)=sin(x);
> sol:=dsolve(deq,y(x));
> simplify(subs(y(x)=rhs(sol),deq));
> #b]
> sol2:=dsolve({deq,y(0)=0,D(y)(0)=-5,(D@@2)(y)(0)=10},y(x));
> #c]
> plot(rhs(sol2),x=-1..1,-6..11);
>
Following are the MAPLE steps to solve Example 2
> deq2:=t^2*diff(x(t),t$2)+t*diff(x(t),t)+(t^2-1/4)*x(t)=t^(3/2);
> sol:=dsolve(deq2,x(t));
> simplify(subs(x(t)=rhs(sol),deq2));
> #b]
> sol2:=dsolve({deq2,x(5)=0,D(x)(5)=2},x(t));
> #c]
> plot(rhs(sol2),t=0..10,x=-2..4);
>