Internal problem ID [3403]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 24
Problem number: 664.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {\left (1-x^{2} y^{2}\right ) y^{\prime }-\left (1+y x \right ) y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 27
dsolve((1-x^2*y(x)^2)*diff(y(x),x) = (1+x*y(x))*y(x)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {1}{x} \\ y \relax (x ) = {\mathrm e}^{-\LambertW \left (-x \,{\mathrm e}^{-c_{1}}\right )-c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 4.928 (sec). Leaf size: 43
DSolve[(1-x^2 y[x]^2)y'[x]==(1+x y[x])y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{x} \\ y(x)\to -\frac {\text {ProductLog}\left (-e^{-c_1} x\right )}{x} \\ y(x)\to 0 \\ y(x)\to -\frac {1}{x} \\ \end{align*}