ODE No. 822

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

✓ Mathematica : cpu = 0.278402 (sec), leaf count = 32

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

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

✓ Maple : cpu = 0.109 (sec), leaf count = 25

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

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