Internal problem ID [2254]
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 1.
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-20 \cos \left (4 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)-16*y(x)=20*cos(4*x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{-4 x}+{\mathrm e}^{4 x} c_{1}-\frac {5 \cos \left (4 x \right )}{8} \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 30
DSolve[y''[x]-16*y[x]==20*Cos[4*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {5}{8} \cos (4 x)+c_1 e^{4 x}+c_2 e^{-4 x} \\ \end{align*}