Internal problem ID [5361]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.2 THE NATURE OF SOLUTIONS.
Page 9
Problem number: 1(k).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {2 x y y^{\prime }-x^{2}-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(2*x*y(x)*diff(y(x),x)=x^2+y(x)^2,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: 0.288 (sec). Leaf size: 38
DSolve[2*x*y[x]*y'[x]==x^2+y[x]^2,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*}