Internal problem ID [2064]
Book: Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section: 1.8, page 68
Problem number: 9.
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 (3 x -y\right ) y^{\prime }-3 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 17
dsolve((3*x-y(x))*diff(y(x),x)=3*y(x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\LambertW \left (-3 x \,{\mathrm e}^{-3 c_{1}}\right )+3 c_{1}} \]
✓ Solution by Mathematica
Time used: 60.018 (sec). Leaf size: 20
DSolve[(3*x-y[x])*y'[x]==3*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{\text {ProductLog}\left (-3 e^{-c_1} x\right )+c_1} \\ \end{align*}