Internal problem ID [3402]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 24
Problem number: 663.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {\left (1-x^{2} y^{2}\right ) y^{\prime }-x y^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 21
dsolve((1-x^2*y(x)^2)*diff(y(x),x) = x*y(x)^3,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\frac {\LambertW \left (-x^{2} {\mathrm e}^{-2 c_{1}}\right )}{2}-c_{1}} \]
✓ Solution by Mathematica
Time used: 60.087 (sec). Leaf size: 55
DSolve[(1-x^2 y[x]^2)y'[x]==x y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {i \sqrt {\text {ProductLog}\left (-e^{-2 c_1} x^2\right )}}{x} \\ y(x)\to \frac {i \sqrt {\text {ProductLog}\left (-e^{-2 c_1} x^2\right )}}{x} \\ \end{align*}