12.1.9 problem 4(a)

Internal problem ID [1527]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 1, Introduction. Section 1.2 Page 14
Problem number : 4(a)
Date solved : Monday, January 27, 2025 at 04:58:55 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: 0.006 (sec). Leaf size: 11

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

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

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 13

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

\[ y(x)\to -e^x (x-1) \]