Internal problem ID [14116]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 1. Introduction to Differential Equations. Review exercises, page
23
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }=x \,{\mathrm e}^{-x^{2}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(diff(y(x),x)=x*exp(-x^2),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{-x^{2}}}{2}+c_{1} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 19
DSolve[y'[x]==x*Exp[-x^2],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {e^{-x^2}}{2}+c_1 \]