Internal problem ID [8449]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 869.
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 +1-2 y+3 x^{2}-2 y x^{2}+2 x^{4}+x^{3}-2 y x^{3}+2 x^{5}}{x^{2}-y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(diff(y(x),x) = 1/(x^2-y(x))*(-x+1-2*y(x)+3*x^2-2*x^2*y(x)+2*x^4+x^3-2*x^3*y(x)+2*x^5),y(x), singsol=all)
\[ y \relax (x ) = x^{2}+\frac {\LambertW \left (-2 \,{\mathrm e}^{x^{4}} {\mathrm e}^{\frac {4 x^{3}}{3}} {\mathrm e}^{-2 x^{2}} c_{1} {\mathrm e}^{4 x} {\mathrm e}^{-1}\right )}{2}+\frac {1}{2} \]
✓ Solution by Mathematica
Time used: 60.034 (sec). Leaf size: 42
DSolve[y'[x] == (1 - x + 3*x^2 + x^3 + 2*x^4 + 2*x^5 - 2*y[x] - 2*x^2*y[x] - 2*x^3*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^{x^4+\frac {4 x^3}{3}-2 x^2+4 x-1+c_1}\right )\right ) \\ \end{align*}