Internal problem ID [3768]
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]
\[ \boxed {y y^{\prime } x +x^{2} {\mathrm e}^{-\frac {2 y}{x}}-y^{2}=0} \]
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = \frac {\left (\operatorname {LambertW}\left (-4 \left (\ln \left (x \right )+c_{1} \right ) {\mathrm e}^{-1}\right )+1\right ) x}{2} \]
✓ Solution by Mathematica
Time used: 60.225 (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]
\[ y(x)\to \frac {1}{2} x \left (1+W\left (\frac {4 (-\log (x)+c_1)}{e}\right )\right ) \]