Internal problem ID [2262]
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 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime }+5 y-4 \cos \left (2 x \right ) {\mathrm e}^{-x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 43
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+5*y(x)=4*exp(-x)*cos(2*x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x} \sin \left (2 x \right ) c_{2}+{\mathrm e}^{-x} \cos \left (2 x \right ) c_{1}+\frac {{\mathrm e}^{-x} \left (2 \sin \left (2 x \right ) x +\cos \left (2 x \right )\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 36
DSolve[y''[x]+2*y'[x]+5*y[x]==4*Exp[-x]*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} e^{-x} ((1+4 c_2) \cos (2 x)+4 (x+c_1) \sin (2 x)) \\ \end{align*}