Internal problem ID [8348]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 768.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]], [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y \left (1+y\right )}{x \left (-y-1+x y\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 26
dsolve(diff(y(x),x) = y(x)*(y(x)+1)/x/(-y(x)-1+x*y(x)),y(x), singsol=all)
\[ y \relax (x ) = -\frac {1}{x \LambertW \left (\frac {{\mathrm e}^{-\frac {1}{x}}}{x c_{1}}\right )+1} \]
✓ Solution by Mathematica
Time used: 1.134 (sec). Leaf size: 66
DSolve[y'[x] == (y[x]*(1 + y[x]))/(x*(-1 - y[x] + x*y[x])),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {2^{2/3} \left (x y(x) \left (-\log \left (\frac {x y(x)}{(x-1) y(x)-1}\right )+\log \left (\frac {y(x)+1}{-x y(x)+y(x)+1}\right )+\log (x)+1\right )-1\right )}{9 x y(x)}=c_1,y(x)\right ] \]