Internal problem ID [6676]
Book: Second order enumerated odes
Section: section 1
Problem number: 43.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y-\sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 22
dsolve(diff(y(x),x$2)+y(x)=sin(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} \sin \relax (x )+\cos \relax (x ) c_{1}+\frac {\sin \relax (x )}{2}-\frac {x \cos \relax (x )}{2} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 22
DSolve[y''[x]+y[x]==Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (-\frac {x}{2}+c_1\right ) \cos (x)+c_2 \sin (x) \\ \end{align*}