Internal problem ID [2570]
Book: Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section: Chapter 11.3, page 316
Problem number: 28.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime } y x -2 x^{2}+y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 30
dsolve(x*y(x)*diff(y(x),x)=2*x^2-y(x)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {x^{4}+c_{1}}}{x} \\ y \relax (x ) = -\frac {\sqrt {x^{4}+c_{1}}}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.17 (sec). Leaf size: 38
DSolve[x*y[x]*y'[x]==2*x^2-y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {x^4+c_1}}{x} \\ y(x)\to \frac {\sqrt {x^4+c_1}}{x} \\ \end{align*}