Internal problem ID [84]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 6.
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: 0.008 (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: 37.945 (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*}