Internal problem ID [1885]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 5, page 21
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y+y^{\prime } x -x y \left (y^{\prime }-1\right )=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 19
dsolve(y(x)+x*diff(y(x),x)=x*y(x)*(diff(y(x),x)-1),y(x), singsol=all)
\[ y \left (x \right ) = -\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-x}}{c_{1} x}\right ) \]
✓ Solution by Mathematica
Time used: 3.033 (sec). Leaf size: 28
DSolve[y[x]+x*y'[x]==x*y[x]*(y'[x]-1),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -W\left (-\frac {e^{-x-c_1}}{x}\right ) \\ y(x)\to 0 \\ \end{align*}