Internal problem ID [2605]
Book: Differential equations with applications and historial notes, George F. Simmons,
1971
Section: Chapter 2, End of chapter, page 61
Problem number: 2.
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 {\left (-y x +1\right ) y^{\prime }-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 19
dsolve((1-x*y(x))*diff(y(x),x)=y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\LambertW \left (-x \,{\mathrm e}^{-c_{1}}\right )-c_{1}} \]
✓ Solution by Mathematica
Time used: 60.091 (sec). Leaf size: 20
DSolve[(1-x*y[x])*y'[x]==y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\text {ProductLog}\left (-e^{-c_1} x\right )}{x} \\ \end{align*}