Internal problem ID [3763]
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`]]
\[ \boxed {y y^{\prime } x -2 y x -y^{2}=-2 x^{2}} \]
✓ Solution by Maple
Time used: 0.031 (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)
\[ y \left (x \right ) = {\mathrm e}^{-\operatorname {LambertW}\left ({\mathrm e}^{2 c_{1}} {\mathrm e}^{-1} x^{2}\right )+2 c_{1} -1} x^{3}+x \]
✓ Solution by Mathematica
Time used: 3.881 (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+W\left (e^{-1+c_1} x^2\right )\right ) y(x)\to x \end{align*}