Internal problem ID [3886]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 4
Problem number: 7.1.
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 (x^{2} y^{2}+y x \right ) y+\left (x^{2} y^{2}-1\right ) x y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 27
dsolve((x^2*y(x)^2+x*y(x))*y(x)+(x^2*y(x)^2-1)*x*diff(y(x),x)=0,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: 60.068 (sec). Leaf size: 29
DSolve[(x^2*y[x]^2+x*y[x])*y[x]+(x^2*y[x]^2-1)*x*y'[x]==0,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} \\ \end{align*}