Internal problem ID [3260]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 19
Problem number: 516.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime } y x +x^{2} {\mathrm e}^{-\frac {2 y}{x}}-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 18
dsolve(x*y(x)*diff(y(x),x)+x^2*exp(-2*y(x)/x)-y(x)^2 = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (\LambertW \left (-4 \left (\ln \relax (x )+c_{1}\right ) {\mathrm e}^{-1}\right )+1\right ) x}{2} \]
✓ Solution by Mathematica
Time used: 0.149 (sec). Leaf size: 25
DSolve[x y[x] y'[x]+x^2 Exp[(-2 y[x])/x]-y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} x \left (1+\text {ProductLog}\left (\frac {4 (-\log (x)+c_1)}{e}\right )\right ) \\ \end{align*}