Internal problem ID [3885]
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`]]
\[ \boxed {\left (x^{2} y^{2}+x y\right ) y+\left (x^{2} y^{2}-1\right ) x y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (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 \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: 2.068 (sec). Leaf size: 43
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 {W\left (-e^{-c_1} x\right )}{x} \\ y(x)\to 0 \\ y(x)\to -\frac {1}{x} \\ \end{align*}