Internal problem ID [2322]
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 27.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-4 y-5 \,{\mathrm e}^{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)-4*y(x)=5*exp(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{-2 x}+c_{1} {\mathrm e}^{2 x}-\frac {5 \,{\mathrm e}^{x}}{3} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 29
DSolve[y''[x]-4*y[x]==5*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {5 e^x}{3}+c_1 e^{2 x}+c_2 e^{-2 x} \\ \end{align*}