Internal problem ID [5747]
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]
\[ \boxed {y^{2}+x y^{2}+\left (x^{2}-y x^{2}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = {\mathrm e}^{\frac {\ln \left (x \right ) x +\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-c_{1} +\frac {1}{x}}}{x}\right ) x +c_{1} x -1}{x}} \]
✓ Solution by Mathematica
Time used: 5.623 (sec). Leaf size: 30
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}{W\left (-\frac {e^{\frac {1}{x}-c_1}}{x}\right )} y(x)\to 0 \end{align*}