Internal problem ID [13444]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 8. Review exercises for part of part II. page 143
Problem number: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {x y y^{\prime }-2 y^{2}=2 x^{2}} \]
✓ Solution by Maple
Time used: 0.015 (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 \left (x \right ) &= \sqrt {c_{1} x^{2}-2}\, x \\ y \left (x \right ) &= -\sqrt {c_{1} x^{2}-2}\, x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.42 (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 -x \sqrt {-2+c_1 x^2} \\ y(x)\to x \sqrt {-2+c_1 x^2} \\ \end{align*}