Internal problem ID [12159]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 1, First-Order Differential Equations. Problems page 88
Problem number: Problem 62.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {\left (y^{2}-x^{2}\right ) y^{\prime }+2 y x=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 47
dsolve((y(x)^2-x^2)*diff(y(x),x)+2*x*y(x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {1-\sqrt {-4 c_{1}^{2} x^{2}+1}}{2 c_{1}} \\ y \left (x \right ) &= \frac {1+\sqrt {-4 c_{1}^{2} x^{2}+1}}{2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.683 (sec). Leaf size: 66
DSolve[(y[x]^2-x^2)*y'[x]+2*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (e^{c_1}-\sqrt {-4 x^2+e^{2 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*}