Internal problem ID [7841]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 261.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {\left (2 y x^{2}-x \right ) y^{\prime }-2 x y^{2}-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 18
dsolve((2*x^2*y(x)-x)*diff(y(x),x)-2*x*y(x)^2-y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {1}{2 \LambertW \left (-\frac {c_{1}}{2 x^{2}}\right ) x} \]
✓ Solution by Mathematica
Time used: 60.485 (sec). Leaf size: 32
DSolve[(2*x^2*y[x]-x)*y'[x]-2*x*y[x]^2-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2 x \text {ProductLog}\left (\frac {e^{-1+\frac {9 c_1}{2^{2/3}}}}{x^2}\right )} \\ \end{align*}