Internal problem ID [3889]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 5
Problem number: 1.2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {-2 y y^{\prime } x +y^{2}+x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve((x^2+y(x)^2)-2*x*y(x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {x^{2}+c_{1} x} \\ y \relax (x ) = -\sqrt {x^{2}+c_{1} x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.212 (sec). Leaf size: 38
DSolve[(x^2+y[x]^2)-2*x*y[x]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {x} \sqrt {x+c_1} \\ y(x)\to \sqrt {x} \sqrt {x+c_1} \\ \end{align*}