Internal problem ID [5040]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems.
page 12
Problem number: Example 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {2 x y^{\prime } \left (x -y^{2}\right )+y^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.037 (sec). Leaf size: 19
dsolve(2*x*diff(y(x),x)*(x-y(x)^2)+y(x)^3=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\frac {\LambertW \left (-\frac {{\mathrm e}^{c_{1}}}{x}\right )}{2}+\frac {c_{1}}{2}} \]
✓ Solution by Mathematica
Time used: 23.308 (sec). Leaf size: 60
DSolve[2*x*y'[x]*(x-y[x]^2)+y[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -i \sqrt {x} \sqrt {\text {ProductLog}\left (-\frac {e^{c_1}}{x}\right )} \\ y(x)\to i \sqrt {x} \sqrt {\text {ProductLog}\left (-\frac {e^{c_1}}{x}\right )} \\ y(x)\to 0 \\ \end{align*}