8.1.10 problem 10

Internal problem ID [660]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.2. Integrals as general and particular solutions. Page 16
Problem number : 10
Date solved : Monday, January 27, 2025 at 02:56:49 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: 0.007 (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: 0.005 (sec). Leaf size: 21

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

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