Internal problem ID [3911]
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`]]
\[ \boxed {\left (1-x^{2} y^{2}\right ) y^{\prime }-\left (y x +1\right ) y^{2}=0} \]
✓ Solution by Maple
Time used: 0.015 (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 \left (x \right ) = -\frac {1}{x} y \left (x \right ) = {\mathrm e}^{-\operatorname {LambertW}\left (-x \,{\mathrm e}^{-c_{1}}\right )-c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 2.179 (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 {W\left (-e^{-c_1} x\right )}{x} y(x)\to 0 y(x)\to -\frac {1}{x} \end{align*}