Internal problem ID [3208]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 17
Problem number: 462.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {\left (x -2 y\right ) y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 17
dsolve((x-2*y(x))*diff(y(x),x) = y(x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\LambertW \left (-\frac {x \,{\mathrm e}^{-\frac {c_{1}}{2}}}{2}\right )+\frac {c_{1}}{2}} \]
✓ Solution by Mathematica
Time used: 10.406 (sec). Leaf size: 31
DSolve[(x-2 y[x])y'[x]==y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x}{2 \text {ProductLog}\left (-\frac {1}{2} e^{-\frac {c_1}{2}} x\right )} \\ y(x)\to 0 \\ \end{align*}