Internal problem ID [4197]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 33
Problem number: 964.
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: 31
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 ) = \frac {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: 0.146 (sec). Leaf size: 50
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 \frac {c_1}{x} y(x)\to -\sqrt {x^2+2 c_1} y(x)\to \sqrt {x^2+2 c_1} y(x)\to 0 \end{align*}