Internal problem ID [877]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }=-{\mathrm e}^{x} x} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 11
dsolve([diff(y(x),x) = -x*exp(x),y(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = -\left (x -1\right ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 13
DSolve[{y'[x] == -x*Exp[x],y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -e^x (x-1) \]