64.1.13 problem 6(a)

Internal problem ID [13258]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 1, Differential equations and their solutions. Exercises page 13
Problem number : 6(a)
Date solved : Tuesday, January 28, 2025 at 05:13:19 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+2 y&=6 \,{\mathrm e}^{x}+4 x \,{\mathrm e}^{-2 x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

dsolve(diff(y(x),x)+2*y(x)=6*exp(x)+4*x*exp(-2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.089 (sec). Leaf size: 26

DSolve[D[y[x],x]+2*y[x]==6*Exp[x]+4*x*Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (2 x^2+2 e^{3 x}+c_1\right ) \]