Internal problem ID [4181]
Book: A treatise on ordinary and partial differential equations by William Woolsey Johnson.
1913
Section: Chapter 2, Equations of the first order and degree. page 20
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{2}+y^{2} x +\left (x^{2}-y x^{2}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.03 (sec). Leaf size: 34
dsolve((y(x)^2+x*y(x)^2)+(x^2-y(x)*x^2)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\frac {\LambertW \left (-\frac {{\mathrm e}^{-c_{1}+\frac {1}{x}}}{x}\right ) x +\ln \relax (x ) x +c_{1} x -1}{x}} \]
✓ Solution by Mathematica
Time used: 0.101 (sec). Leaf size: 25
DSolve[(y[x]^2+x*y[x]^2)+(x^2-y[x]*x^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\text {ProductLog}\left (-\frac {e^{\frac {1}{x}-c_1}}{x}\right )} \\ \end{align*}