Internal problem ID [8317]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 737.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x),G(x)]], [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x \left (-1+x -2 y x +2 x^{3}\right )}{x^{2}-y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(x),x) = 1/(x^2-y(x))*x*(-1+x-2*x*y(x)+2*x^3),y(x), singsol=all)
\[ y \relax (x ) = x^{2}+\frac {\LambertW \left (-2 \,{\mathrm e}^{\frac {4 x^{3}}{3}} {\mathrm e}^{-2 x^{2}} c_{1} {\mathrm e}^{-1}\right )}{2}+\frac {1}{2} \]
✓ Solution by Mathematica
Time used: 60.025 (sec). Leaf size: 36
DSolve[y'[x] == (x*(-1 + x + 2*x^3 - 2*x*y[x]))/(x^2 - y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2+\frac {1}{2} \left (1+\text {ProductLog}\left (-e^{\frac {4 x^3}{3}-2 x^2-1+c_1}\right )\right ) \\ \end{align*}