Internal problem ID [2072]
Book: Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section: 1.8, page 68
Problem number: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A]]
Solve \begin {gather*} \boxed {2 y y^{\prime } x -2 y^{2}-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 26
dsolve(2*x*y(x)*diff(y(x),x)-(x^2*exp(-y(x)^2/x^2)+2*y(x)^2)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {\ln \left (\ln \relax (x )+c_{1}\right )}\, x \\ y \relax (x ) = -\sqrt {\ln \left (\ln \relax (x )+c_{1}\right )}\, x \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.202 (sec). Leaf size: 38
DSolve[2*x*y[x]*y'[x]-(x^2*Exp[-y[x]^2/x^2]+2*y[x]^2)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \sqrt {\log (\log (x)+2 c_1)} \\ y(x)\to x \sqrt {\log (\log (x)+2 c_1)} \\ \end{align*}