Internal problem ID [3879]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 4
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {2 y x +\left (y^{2}-2 x^{2}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.02 (sec). Leaf size: 19
dsolve(2*x*y(x)+(y(x)^2-2*x^2)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \sqrt {-\frac {2}{\LambertW \left (-2 c_{1} x^{2}\right )}}\, x \]
✓ Solution by Mathematica
Time used: 20.146 (sec). Leaf size: 66
DSolve[2*x*y[x]+(y[x]^2-2*x^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {i \sqrt {2} x}{\sqrt {\text {ProductLog}\left (-2 e^{-2 c_1} x^2\right )}} \\ y(x)\to \frac {i \sqrt {2} x}{\sqrt {\text {ProductLog}\left (-2 e^{-2 c_1} x^2\right )}} \\ y(x)\to 0 \\ \end{align*}