50.11.3 problem 1(c)

Internal problem ID [7987]
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)
Date solved : Monday, January 27, 2025 at 03:35:41 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=64 x \,{\mathrm e}^{-x} \end{align*}

✓ Solution by Maple

Time used: 0.007 (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)
 

\[ y = \left (-8 x^{2}+c_{1} -4 x \right ) {\mathrm e}^{-x}+{\mathrm e}^{3 x} c_{2} \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 31

DSolve[D[y[x],{x,2}]-2*D[y[x],x]-3*y[x]==64*x*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (-8 x^2-4 x+c_2 e^{4 x}-1+c_1\right ) \]