Internal problem ID [4994]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.1 Separable equations problems. page
7
Problem number: 34.
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: 0.019 (sec). Leaf size: 34
dsolve((y(x)^2+x*y(x)^2)+(x^2-x^2*y(x))*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: 0.091 (sec). Leaf size: 25
DSolve[(y[x]^2+x*y[x]^2)+(x^2-x^2*y[x])*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*}