Internal problem ID [5367]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.2 THE NATURE OF SOLUTIONS.
Page 9
Problem number: 2(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-{\mathrm e}^{x^{2}} x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
dsolve(diff(y(x),x)=x*exp(x^2),y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{x^{2}}}{2}+c_{1} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 17
DSolve[y'[x]==x*Exp[x^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{x^2}}{2}+c_1 \\ \end{align*}