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]
\[ \boxed {\left (1-y^{2} x^{2}\right ) y^{\prime }-x y^{3}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve((1-x^2*y(x)^2)*diff(y(x),x) = x*y(x)^3,y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{-c_{1}}}{\sqrt {-\frac {{\mathrm e}^{-2 c_{1}} x^{2}}{\operatorname {LambertW}\left (-{\mathrm e}^{-2 c_{1}} x^{2}\right )}}} \]
✓ 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*}