Internal problem ID [6319]
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]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }-3 y=64 x \,{\mathrm e}^{-x}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)-2*diff(y(x),x)-3*y(x)=64*x*exp(-x),y(x), singsol=all)
\[ y \left (x \right ) = \left (-8 x^{2}+c_{1} -4 x \right ) {\mathrm e}^{-x}+c_{2} {\mathrm e}^{3 x} \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 31
DSolve[y''[x]-2*y'[x]-3*y[x]==64*x*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (-8 x^2-4 x+c_2 e^{4 x}-1+c_1\right ) \]