ODE No. 262

\[ 2 x^3+\left (2 x^2 y(x)-x^3\right ) y'(x)-4 x y(x)^2+y(x)^3=0 \] Mathematica : cpu = 0.170012 (sec), leaf count = 101

DSolve[2*x^3 - 4*x*y[x]^2 + y[x]^3 + (-x^3 + 2*x^2*y[x])*Derivative[1][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to \frac {2 x^3-\sqrt {e^{4 c_1} x^2-3 e^{2 c_1} x^4}}{x^2+e^{2 c_1}}\right \},\left \{y(x)\to \frac {2 x^3+\sqrt {e^{4 c_1} x^2-3 e^{2 c_1} x^4}}{x^2+e^{2 c_1}}\right \}\right \}\] Maple : cpu = 0.222 (sec), leaf count = 65

dsolve((2*x^2*y(x)-x^3)*diff(y(x),x)+y(x)^3-4*x*y(x)^2+2*x^3 = 0,y(x))
 

\[y \left (x \right ) = \frac {x \left (2 x^{2} c_{1}-\sqrt {3 x^{2} c_{1}+1}\right )}{x^{2} c_{1}-1}\]