Internal problem ID [7881]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 301.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {\left (6 x y^{2}+x^{2}\right ) y^{\prime }-y \left (3 y^{2}-x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 25
dsolve((6*x*y(x)^2+x^2)*diff(y(x),x)-y(x)*(3*y(x)^2-x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{-\frac {\LambertW \left (\frac {6 \,{\mathrm e}^{3 c_{1}}}{x^{3}}\right )}{2}+\frac {3 c_{1}}{2}}}{x} \]
✓ Solution by Mathematica
Time used: 59.862 (sec). Leaf size: 69
DSolve[(6*x*y[x]^2+x^2)*y'[x]-y[x]*(3*y[x]^2-x)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {x} \sqrt {\text {ProductLog}\left (\frac {6 e^{3 c_1}}{x^3}\right )}}{\sqrt {6}} \\ y(x)\to \frac {\sqrt {x} \sqrt {\text {ProductLog}\left (\frac {6 e^{3 c_1}}{x^3}\right )}}{\sqrt {6}} \\ y(x)\to 0 \\ \end{align*}