Internal problem ID [2264]
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 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+16 y-34 \,{\mathrm e}^{x}-16 \cos \left (4 x \right )+8 \sin \left (4 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 38
dsolve(diff(y(x),x$2)+16*y(x)=34*exp(x)+16*cos(4*x)-8*sin(4*x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} \sin \left (4 x \right )+\cos \left (4 x \right ) c_{1}+\frac {\left (8 x -1\right ) \sin \left (4 x \right )}{4}+\cos \left (4 x \right ) x +2 \,{\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.249 (sec). Leaf size: 37
DSolve[y''[x]+16*y[x]==34*Exp[x]+16*Cos[4*x]-8*Sin[4*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 e^x+\left (x+\frac {1}{4}+c_1\right ) \cos (4 x)+\left (2 x-\frac {1}{8}+c_2\right ) \sin (4 x) \\ \end{align*}