Internal problem ID [83]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 5.
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 {x \left (x +y\right ) y^{\prime }-y \left (x -y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve(x*(x+y(x))*diff(y(x),x) = y(x)*(x-y(x)),y(x), singsol=all)
\[ y \relax (x ) = \frac {x}{\LambertW \left (c_{1} x^{2}\right )} \]
✓ Solution by Mathematica
Time used: 60.076 (sec). Leaf size: 20
DSolve[x*(x+y[x])*y'[x] == y[x]*(x-y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x}{\text {ProductLog}\left (e^{-c_1} x^2\right )} \\ \end{align*}