Internal problem ID [3341]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 21
Problem number: 599.
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 }-y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 16
dsolve((x^2+y(x)^2)*diff(y(x),x) = x*y(x),y(x), singsol=all)
\[ y \relax (x ) = \sqrt {\frac {1}{\LambertW \left (c_{1} x^{2}\right )}}\, x \]
✓ Solution by Mathematica
Time used: 19.634 (sec). Leaf size: 49
DSolve[(x^2+y[x]^2)y'[x]==x y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x}{\sqrt {\text {ProductLog}\left (e^{-2 c_1} x^2\right )}} \\ y(x)\to \frac {x}{\sqrt {\text {ProductLog}\left (e^{-2 c_1} x^2\right )}} \\ y(x)\to 0 \\ \end{align*}