Internal problem ID [3910]
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]
\[ \boxed {\left (1-x^{2} y^{2}\right ) y^{\prime }-y^{3} x=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve((1-x^2*y(x)^2)*diff(y(x),x) = x*y(x)^3,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-\frac {\operatorname {LambertW}\left (-x^{2} {\mathrm e}^{-2 c_{1}}\right )}{2}-c_{1}} \]
✓ Solution by Mathematica
Time used: 5.286 (sec). Leaf size: 60
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 {W\left (-e^{-2 c_1} x^2\right )}}{x} y(x)\to \frac {i \sqrt {W\left (-e^{-2 c_1} x^2\right )}}{x} y(x)\to 0 \end{align*}