50.10.5 problem 1(e)

Internal problem ID [7974]
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)
Date solved : Monday, January 27, 2025 at 03:34:49 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=20 \,{\mathrm e}^{-2 x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 20

dsolve(diff(y(x),x$2)-diff(y(x),x)-6*y(x)=20*exp(-2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 32

DSolve[D[y[x],{x,2}]-D[y[x],x]-6*y[x]==20*Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{5} e^{-2 x} \left (-20 x+5 c_2 e^{5 x}-4+5 c_1\right ) \]