Internal problem ID [4196]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 33
Problem number: 963.
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: 33
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: 0.06 (sec). Leaf size: 65
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 -i x y(x)\to i x \end{align*}