Internal problem ID [4356]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 2
Problem number: 1.2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{2}+y^{2} x +\left (x^{2}-x^{2} y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 34
dsolve((y(x)^2+x*y(x)^2)+(x^2-y(x)*x^2)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{\frac {x \ln \left (x \right )+\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-c_{1} +\frac {1}{x}}}{x}\right ) x +c_{1} x -1}{x}} \]
✓ Solution by Mathematica
Time used: 5.328 (sec). Leaf size: 30
DSolve[(y[x]^2+x*y[x]^2)+(x^2-y[x]*x^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{W\left (-\frac {e^{\frac {1}{x}-c_1}}{x}\right )} y(x)\to 0 \end{align*}