Internal problem ID [5553]
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 2.2. THE METHOD OF UNDETERMINED
COEFFICIENTS. Page 67
Problem number: 1(e).
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-20 \,{\mathrm e}^{-2 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)-diff(y(x),x)-6*y(x)=20*exp(-2*x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{3 x}+{\mathrm e}^{-2 x} c_{1}-4 \,{\mathrm e}^{-2 x} x \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 32
DSolve[y''[x]-y'[x]-6*y[x]==20*Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{5} e^{-2 x} \left (-20 x+5 c_2 e^{5 x}-4+5 c_1\right ) \\ \end{align*}