Internal problem ID [5566]
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: 1(c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }-3 y-64 \,{\mathrm e}^{-x} x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x$2)-2*diff(y(x),x)-3*y(x)=64*x*exp(-x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{-x}+c_{1} {\mathrm e}^{3 x}+\left (-8 x^{2}-4 x \right ) {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 31
DSolve[y''[x]-2*y'[x]-3*y[x]==64*x*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} \left (-4 x (2 x+1)+c_2 e^{4 x}-1+c_1\right ) \\ \end{align*}