31.3.8 problem 7.1

Internal problem ID [5738]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 4
Problem number : 7.1
Date solved : Monday, January 27, 2025 at 01:12:18 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} \left (x^{2} y^{2}+y x \right ) y+\left (x^{2} y^{2}-1\right ) x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.022 (sec). Leaf size: 25

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 ) &= -\frac {\operatorname {LambertW}\left (-x \,{\mathrm e}^{-c_{1}}\right )}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.971 (sec). Leaf size: 43

DSolve[(x^2*y[x]^2+x*y[x])*y[x]+(x^2*y[x]^2-1)*x*D[y[x],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*}