2.306   ODE No. 306

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

✓ Mathematica : cpu = 0.10313 (sec), leaf count = 201

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

\[\left \{\left \{y(x)\to \sqrt [3]{x^3-\sqrt {x^6-e^{6 c_1}}}\right \},\left \{y(x)\to -\sqrt [3]{-1} \sqrt [3]{x^3-\sqrt {x^6-e^{6 c_1}}}\right \},\left \{y(x)\to (-1)^{2/3} \sqrt [3]{x^3-\sqrt {x^6-e^{6 c_1}}}\right \},\left \{y(x)\to \sqrt [3]{x^3+\sqrt {x^6-e^{6 c_1}}}\right \},\left \{y(x)\to -\sqrt [3]{-1} \sqrt [3]{x^3+\sqrt {x^6-e^{6 c_1}}}\right \},\left \{y(x)\to (-1)^{2/3} \sqrt [3]{x^3+\sqrt {x^6-e^{6 c_1}}}\right \}\right \}\]

✓ Maple : cpu = 0.98 (sec), leaf count = 225

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

\[y \left (x \right ) = \frac {x}{\left (x^{3} c_{1} \left (-x^{3} c_{1} +\sqrt {c_{1}^{2} x^{6}+1}\right )\right )^{{1}/{3}}}\]