Internal problem ID [3672]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 15
Problem number: 418.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y y^{\prime }=-x \,{\mathrm e}^{x^{2}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(y(x)*diff(y(x),x)+x*exp(x^2) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \sqrt {-{\mathrm e}^{x^{2}}+c_{1}} y \left (x \right ) = -\sqrt {-{\mathrm e}^{x^{2}}+c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 1.743 (sec). Leaf size: 43
DSolve[y[x] y'[x]+x Exp[x^2]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-e^{x^2}+2 c_1} y(x)\to \sqrt {-e^{x^2}+2 c_1} \end{align*}