Internal problem ID [3255]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 18
Problem number: 511.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {y^{\prime } y x +2 x^{2}-2 y x -y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 29
dsolve(x*y(x)*diff(y(x),x)+2*x^2-2*x*y(x)-y(x)^2 = 0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\LambertW \left ({\mathrm e}^{2 c_{1}} {\mathrm e}^{-1} x^{2}\right )+2 c_{1}-1} x^{3}+x \]
✓ Solution by Mathematica
Time used: 10.903 (sec). Leaf size: 25
DSolve[x y[x] y'[x]+2 x^2-2 x y[x]-y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \left (1+\text {ProductLog}\left (e^{-1+c_1} x^2\right )\right ) \\ y(x)\to x \\ \end{align*}