Internal problem ID [8585]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1005.
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 (a x \right ) \sin \left (x b \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 82
dsolve(diff(diff(y(x),x),x)+y(x)-sin(a*x)*sin(b*x)=0,y(x), singsol=all)
\[ y \relax (x ) = \sin \relax (x ) c_{2}+\cos \relax (x ) c_{1}+\frac {-\left (a +b +1\right ) \left (a +b -1\right ) \cos \left (x \left (a -b \right )\right )+\cos \left (x \left (a +b \right )\right ) \left (a -b +1\right ) \left (a -b -1\right )}{2 a^{4}+\left (-4 b^{2}-4\right ) a^{2}+2 b^{4}-4 b^{2}+2} \]
✓ Solution by Mathematica
Time used: 0.284 (sec). Leaf size: 92
DSolve[-(Sin[a*x]*Sin[b*x]) + y[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-\left (a^2+b^2-1\right ) \sin (a x) \sin (b x)-2 a b \cos (a x) \cos (b x)+(a-b-1) (a-b+1) (a+b-1) (a+b+1) (c_1 \cos (x)+c_2 \sin (x))}{-2 \left (a^2+1\right ) b^2+\left (a^2-1\right )^2+b^4} \\ \end{align*}