Internal problem ID [2324]
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 8.10, Chapter review. page
575
Problem number: Problem 29.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y-4 \,{\mathrm e}^{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(diff(y(x),x$2)-y(x)=4*exp(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{-x}+{\mathrm e}^{x} c_{1}+2 x \,{\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 25
DSolve[y''[x]-y[x]==4*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x (2 x-1+c_1)+c_2 e^{-x} \\ \end{align*}