50.11.15 problem 4

Internal problem ID [7999]
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
Date solved : Monday, January 27, 2025 at 03:36:29 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&={\mathrm e}^{-x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 23

dsolve(diff(y(x),x$2)-diff(y(x),x)-6*y(x)=exp(-x),y(x), singsol=all)
 

\[ y = -\frac {\left (-4 \,{\mathrm e}^{5 x} c_{2} +{\mathrm e}^{x}-4 c_{1} \right ) {\mathrm e}^{-2 x}}{4} \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 31

DSolve[D[y[x],{x,2}]-D[y[x],x]-6*y[x]==Exp[-x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {e^{-x}}{4}+c_1 e^{-2 x}+c_2 e^{3 x} \]