Internal problem ID [5625]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Problems for Review and Discovery. Drill excercises. Page 105
Problem number: 1(h).
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-{\mathrm e}^{3 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)-y(x)=exp(3*x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{-x}+c_{1} {\mathrm e}^{x}+\frac {{\mathrm e}^{3 x}}{8} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 29
DSolve[y''[x]-y[x]==Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{3 x}}{8}+c_1 e^x+c_2 e^{-x} \\ \end{align*}