Internal problem ID [4418]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page
46
Problem number: 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x +x y^{2}+y \,{\mathrm e}^{x^{2}} y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 35
dsolve((x+x*y(x)^2)+exp(x^2)*y(x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {{\mathrm e}^{{\mathrm e}^{-x^{2}}} c_{1}-1} \\ y \relax (x ) = -\sqrt {{\mathrm e}^{{\mathrm e}^{-x^{2}}} c_{1}-1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 4.569 (sec). Leaf size: 65
DSolve[(x+x*y[x]^2)+Exp[x^2]*y[x]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-1+e^{e^{-x^2}+2 c_1}} \\ y(x)\to \sqrt {-1+e^{e^{-x^2}+2 c_1}} \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}