64.2.3 problem 2(b)

Internal problem ID [13263]
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(b)
Date solved : Tuesday, January 28, 2025 at 05:13:28 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 (-1\right )&={\mathrm e}+3 \end{align*}

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 17

dsolve([diff(y(x),x)+y(x)=2*x*exp(-x),y(-1) = exp(1)+3],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 20

DSolve[{D[y[x],x]+y[x]==2*x*Exp[-x],{y[-1]==Exp[1]+3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x-1} \left (e x^2+3\right ) \]