Internal problem ID [5803]
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: 51.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {y \left (y^{2} x^{2}+1\right )+\left (y^{2} x^{2}-1\right ) x y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 33
dsolve(y(x)*(x^2*y(x)^2+1)+(x^2*y(x)^2-1)*x*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{-2 c_{1}} x}{\sqrt {-\frac {x^{4} {\mathrm e}^{-4 c_{1}}}{\operatorname {LambertW}\left (-x^{4} {\mathrm e}^{-4 c_{1}}\right )}}} \]
✓ Solution by Mathematica
Time used: 31.376 (sec). Leaf size: 60
DSolve[y[x]*(x^2*y[x]^2+1)+(x^2*y[x]^2-1)*x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {i \sqrt {W\left (-e^{-2 c_1} x^4\right )}}{x} \\ y(x)\to \frac {i \sqrt {W\left (-e^{-2 c_1} x^4\right )}}{x} \\ y(x)\to 0 \\ \end{align*}