7.1.10 problem 10

Internal problem ID [10]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.2. Problems at page 17
Problem number : 10
Date solved : Friday, February 07, 2025 at 08:11:47 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 16

dsolve([diff(y(x),x)=x*exp(-x),y(0) = 1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 21

DSolve[{D[y[x],x]==x*Exp[-x],{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

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