Internal problem ID [3309]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 20
Problem number: 567.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {x \left (-y x +1\right ) y^{\prime }+\left (y x +1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve(x*(1-x*y(x))*diff(y(x),x)+(1+x*y(x))*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {1}{\LambertW \left (-\frac {c_{1}}{x^{2}}\right ) x} \]
✓ Solution by Mathematica
Time used: 60.49 (sec). Leaf size: 30
DSolve[x(1-x y[x])y'[x]+(1+x y[x])y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{x \text {ProductLog}\left (\frac {e^{-1+\frac {9 c_1}{2^{2/3}}}}{x^2}\right )} \\ \end{align*}