ODE No. 869

\[ y'(x)=\frac {2 x^5+2 x^4-2 x^3 y(x)+x^3-2 x^2 y(x)+3 x^2-2 y(x)-x+1}{x^2-y(x)} \] Mathematica : cpu = 0.0454136 (sec), leaf count = 42

DSolve[Derivative[1][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]
 

\[\left \{\left \{y(x)\to x^2+\frac {1}{2} \left (1+W\left (-e^{x^4+\frac {4 x^3}{3}-2 x^2+4 x-1+c_1}\right )\right )\right \}\right \}\] Maple : cpu = 0.196 (sec), leaf count = 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))
 

\[y \left (x \right ) = x^{2}+\frac {\LambertW \left (-2 \,{\mathrm e}^{x^{4}} {\mathrm e}^{\frac {4 x^{3}}{3}} {\mathrm e}^{-2 x^{2}} c_{1} {\mathrm e}^{4 x} {\mathrm e}^{-1}\right )}{2}+\frac {1}{2}\]