Internal problem ID [7840]
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`]]
\[ \boxed {\left (2 y x^{2}-x \right ) y^{\prime }-2 y^{2} x -y=0} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = -\frac {1}{2 \operatorname {LambertW}\left (-\frac {c_{1}}{2 x^{2}}\right ) x} \]
✓ Solution by Mathematica
Time used: 5.936 (sec). Leaf size: 37
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 W\left (\frac {e^{-1+\frac {9 c_1}{2^{2/3}}}}{x^2}\right )} \\ y(x)\to 0 \\ \end{align*}