Internal problem ID [3373]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 23
Problem number: 633.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {\left (x^{2}+a y^{2}\right ) y^{\prime }-y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 23
dsolve((x^2+a*y(x)^2)*diff(y(x),x) = x*y(x),y(x), singsol=all)
\[ y \relax (x ) = \sqrt {\frac {1}{a \LambertW \left (\frac {x^{2} c_{1}}{a}\right )}}\, x \]
✓ Solution by Mathematica
Time used: 74.699 (sec). Leaf size: 71
DSolve[(x^2+a y[x]^2)y'[x]==x y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x}{\sqrt {a} \sqrt {\text {ProductLog}\left (\frac {x^2 e^{-\frac {2 c_1}{a}}}{a}\right )}} \\ y(x)\to \frac {x}{\sqrt {a} \sqrt {\text {ProductLog}\left (\frac {x^2 e^{-\frac {2 c_1}{a}}}{a}\right )}} \\ y(x)\to 0 \\ \end{align*}