Internal problem ID [8583]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1003.
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 \left (n x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(diff(y(x),x),x)+y(x)-sin(n*x)=0,y(x), singsol=all)
\[ y \relax (x ) = \sin \relax (x ) c_{2}+\cos \relax (x ) c_{1}-\frac {\sin \left (n x \right )}{n^{2}-1} \]
✓ Solution by Mathematica
Time used: 0.08 (sec). Leaf size: 29
DSolve[-Sin[n*x] + y[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sin (n x)}{n^2-1}+c_1 \cos (x)+c_2 \sin (x) \\ \end{align*}