Internal problem ID [2075]
Book: Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section: 1.8, page 68
Problem number: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {2 x \left (y+2 x \right ) y^{\prime }-y \left (4 x -y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.023 (sec). Leaf size: 25
dsolve(2*x*(y(x)+2*x)*diff(y(x),x)=y(x)*(4*x-y(x)),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\LambertW \left (2 \,{\mathrm e}^{\frac {3 c_{1}}{2}} x^{\frac {3}{2}}\right )-\frac {3 c_{1}}{2}-\frac {3 \ln \relax (x )}{2}} x \]
✓ Solution by Mathematica
Time used: 8.021 (sec). Leaf size: 29
DSolve[2*x*(y[x]+2*x)*y'[x]==y[x]*(4*x-y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 x}{\text {ProductLog}\left (2 e^{-c_1} x^{3/2}\right )} \\ y(x)\to 0 \\ \end{align*}