Internal problem ID [2258]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 8, Linear differential equations of order n. Section 8.4, Complex-Valued Trial
Solutions. page 529
Problem number: Problem 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y^{\prime }-2 y-40 \left (\sin ^{2}\relax (x )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 28
dsolve(diff(y(x),x$2)-diff(y(x),x)-2*y(x)=40*sin(x)^2,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x} c_{2}+c_{1} {\mathrm e}^{2 x}-10+\sin \left (2 x \right )+3 \cos \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 33
DSolve[y''[x]-y'[x]-2*y[x]==40*Sin[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sin (2 x)+3 \cos (2 x)+c_1 e^{-x}+c_2 e^{2 x}-10 \\ \end{align*}