Internal problem ID [998]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable
Equations. Section 2.4 Page 68
Problem number: 21.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2 y^{2}+x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}}{2 y x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 26
dsolve(diff(y(x),x)=(2*y(x)^2+x^2*exp(- (y(x)/x)^2 ))/(2*x*y(x)),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: 2.096 (sec). Leaf size: 38
DSolve[y'[x]==(2*y[x]^2+x^2*Exp[- (y[x]/x)^2 ])/(2*x*y[x]),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*}