Internal problem ID [12122]
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 11.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
\[ \boxed {x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}\right ) y^{\prime }+y x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(x*y(x)*diff(y(x),x)^2-(x^2+y(x)^2)*diff(y(x),x)+x*y(x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= c_{1} x \\ y \left (x \right ) &= \sqrt {x^{2}+c_{1}} \\ y \left (x \right ) &= -\sqrt {x^{2}+c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.17 (sec). Leaf size: 55
DSolve[x*y[x]*y'[x]^2-(x^2+y[x]^2)*y'[x]+x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x \\ y(x)\to -\sqrt {x^2+2 c_1} \\ y(x)\to \sqrt {x^2+2 c_1} \\ y(x)\to -x \\ y(x)\to x \\ \end{align*}