Internal problem ID [14076]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number: 39.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }=x \,{\mathrm e}^{-x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(diff(y(x),x)=x*exp(-x),y(x), singsol=all)
\[ y \left (x \right ) = \left (-x -1\right ) {\mathrm e}^{-x}+c_{1} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 18
DSolve[y'[x]==x*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -e^{-x} (x+1)+c_1 \]