Internal problem ID [7864]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 284.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {\left (4 y^{2}+x^{2}\right ) y^{\prime }-y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 21
dsolve((4*y(x)^2+x^2)*diff(y(x),x)-x*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\frac {\LambertW \left (\frac {x^{2} {\mathrm e}^{2 c_{1}}}{4}\right )}{2}-c_{1}} \]
✓ Solution by Mathematica
Time used: 60.186 (sec). Leaf size: 59
DSolve[(4*y[x]^2+x^2)*y'[x]-x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x}{2 \sqrt {\text {ProductLog}\left (\frac {1}{4} e^{-\frac {c_1}{2}} x^2\right )}} \\ y(x)\to \frac {x}{2 \sqrt {\text {ProductLog}\left (\frac {1}{4} e^{-\frac {c_1}{2}} x^2\right )}} \\ \end{align*}