Internal problem ID [3884]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 4
Problem number: 5.4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {y^{2}+\left (y x +x^{2}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 44
dsolve(y(x)^2+(x*y(x)+x^2)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {1+\sqrt {c_{1} x^{2}+1}}{c_{1} x} \\ y \relax (x ) = -\frac {-1+\sqrt {c_{1} x^{2}+1}}{c_{1} x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.03 (sec). Leaf size: 80
DSolve[y[x]^2+(x*y[x]+x^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{2 c_1}-\sqrt {e^{2 c_1} \left (x^2+e^{2 c_1}\right )}}{x} \\ y(x)\to \frac {\sqrt {e^{2 c_1} \left (x^2+e^{2 c_1}\right )}+e^{2 c_1}}{x} \\ y(x)\to 0 \\ \end{align*}