64.2.2 problem 2(a)

Internal problem ID [13262]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 1, section 1.3. Exercises page 22
Problem number : 2(a)
Date solved : Tuesday, January 28, 2025 at 05:13:26 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} y \left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 14

dsolve([diff(y(x),x)+y(x)=2*x*exp(-x),y(0) = 2],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.058 (sec). Leaf size: 16

DSolve[{D[y[x],x]+y[x]==2*x*Exp[-x],{y[0]==2}},y[x],x,IncludeSingularSolutions -> True]
 

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