Internal problem ID [5000]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems.
page 12
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {\left (x^{2}+y^{2}\right ) y^{\prime }-2 x y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.043 (sec). Leaf size: 45
dsolve((x^2+y(x)^2)*diff(y(x),x)=2*x*y(x),y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {-1+\sqrt {4 c_{1}^{2} x^{2}+1}}{2 c_{1}} \\ y \relax (x ) = \frac {1+\sqrt {4 c_{1}^{2} x^{2}+1}}{2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.409 (sec). Leaf size: 70
DSolve[(x^2+y[x]^2)*y'[x]==2*x*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (-\sqrt {4 x^2+e^{2 c_1}}-e^{c_1}\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {4 x^2+e^{2 c_1}}-e^{c_1}\right ) \\ y(x)\to 0 \\ \end{align*}