29.15.10 problem 418

Internal problem ID [5016]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 15
Problem number : 418
Date solved : Monday, January 27, 2025 at 10:03:42 AM
CAS classification : [_separable]

\begin{align*} y^{\prime } y+x \,{\mathrm e}^{x^{2}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.011 (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: 1.740 (sec). Leaf size: 43

DSolve[y[x] D[y[x],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*}