2.972   ODE No. 972

\[ y'(x)=\frac {x \left (-2 x^4+2 x^2 y(x)-x^2+1\right )}{y(x)-x^2} \]

✓ Mathematica : cpu = 0.0296206 (sec), leaf count = 32

DSolve[Derivative[1][y][x] == (x*(1 - x^2 - 2*x^4 + 2*x^2*y[x]))/(-x^2 + y[x]),y[x],x]
 

\[\left \{\left \{y(x)\to x^2+\frac {1}{2} \left (1+W\left (-e^{x^4-2 x^2-1+c_1}\right )\right )\right \}\right \}\]

✓ Maple : cpu = 0.31 (sec), leaf count = 27

dsolve(diff(y(x),x) = x*(-x^2+2*x^2*y(x)-2*x^4+1)/(y(x)-x^2),y(x))
 

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