Internal problem ID [2261]
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 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-4 y-100 \,{\mathrm e}^{x} \sin \relax (x ) x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 40
dsolve(diff(y(x),x$2)-4*y(x)=100*x*exp(x)*sin(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{2 x}+{\mathrm e}^{-2 x} c_{1}-2 \,{\mathrm e}^{x} \left (5 x \cos \relax (x )+10 \sin \relax (x ) x +7 \cos \relax (x )-\sin \relax (x )\right ) \]
✓ Solution by Mathematica
Time used: 0.05 (sec). Leaf size: 44
DSolve[y''[x]-4*y[x]==100*x*Exp[x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{2 x}+c_2 e^{-2 x}-2 e^x ((10 x-1) \sin (x)+(5 x+7) \cos (x)) \\ \end{align*}