Internal problem ID [9072]
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`]]
\[ \boxed {y^{\prime }-\frac {x \left (-1+x -2 x y+2 x^{3}\right )}{x^{2}-y}=0} \]
✓ 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)
\[ y \left (x \right ) = x^{2}+\frac {\operatorname {LambertW}\left (-2 \,{\mathrm e}^{\frac {4 x^{3}}{3}} {\mathrm e}^{-2 x^{2}} c_{1} {\mathrm e}^{-1}\right )}{2}+\frac {1}{2} \]
✓ Solution by Mathematica
Time used: 3.498 (sec). Leaf size: 47
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+W\left (-e^{\frac {4 x^3}{3}-2 x^2-1+c_1}\right )\right ) y(x)\to x^2+\frac {1}{2} \end{align*}