ODE No. 504

\[ -\left (-a+x^3+y(x)^3\right ) y'(x)+x^2 y(x)+x y(x)^2 y'(x)^2=0 \]

✓ Mathematica : cpu = 0.0508612 (sec), leaf count = 36

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

\[\left \{y(x)\to \frac {\sqrt [3]{c_1} \sqrt [3]{a-x^3+c_1 x^3}}{\sqrt [3]{-1+c_1}}\right \}\]

✓ Maple : cpu = 1.142 (sec), leaf count = 247

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

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