Internal problem ID [5578]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Second-Order Linear Equations. Section 2.3. THE METHOD OF VARIATION OF
PARAMETERS. Page 71
Problem number: 4.
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^{\prime }-6 y-{\mathrm e}^{-x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)-diff(y(x),x)-6*y(x)=exp(-x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{3 x}+{\mathrm e}^{-2 x} c_{1}-\frac {{\mathrm e}^{-x}}{4} \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 31
DSolve[y''[x]-y'[x]-6*y[x]==Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {e^{-x}}{4}+c_1 e^{-2 x}+c_2 e^{3 x} \\ \end{align*}