Internal problem ID [8388]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 808.
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 {\left (1+2 y\right ) \left (1+y\right )}{x \left (-2 y-2+x +2 x y\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.017 (sec). Leaf size: 44
dsolve(diff(y(x),x) = 1/x*(1+2*y(x))*(y(x)+1)/(-2*y(x)-2+x+2*x*y(x)),y(x), singsol=all)
\[ y \relax (x ) = -\frac {x \LambertW \left (\frac {{\mathrm e}^{-\frac {1}{x}}}{x c_{1}}\right )+2}{2 \left (x \LambertW \left (\frac {{\mathrm e}^{-\frac {1}{x}}}{x c_{1}}\right )+1\right )} \]
✓ Solution by Mathematica
Time used: 1.455 (sec). Leaf size: 149
DSolve[y'[x] == ((1 + y[x])*(1 + 2*y[x]))/(x*(-2 + x - 2*y[x] + 2*x*y[x])),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {2^{2/3} \left (x \log \left (-\frac {6\ 2^{2/3} (y(x)+1)}{2 (x-1) y(x)+x-2}\right )-x \log \left (\frac {3\ 2^{2/3} (2 x y(x)+x)}{2 (x-1) y(x)+x-2}\right )+2 x y(x) \left (\log \left (-\frac {6\ 2^{2/3} (y(x)+1)}{2 (x-1) y(x)+x-2}\right )-\log \left (\frac {3\ 2^{2/3} (2 x y(x)+x)}{2 (x-1) y(x)+x-2}\right )+\log (x)+1\right )+x+x \log (x)-1\right )}{9 (2 x y(x)+x)}=c_1,y(x)\right ] \]