2.306   ODE No. 306

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ \left (y(x)^3-x^3\right ) y'(x)-x^2 y(x)=0 \] Mathematica : cpu = 0.155274 (sec), leaf count = 201

\[\left \{\left \{y(x)\to \sqrt [3]{x^3-\sqrt {x^6-e^{6 c_1}}}\right \},\left \{y(x)\to -\sqrt [3]{-1} \sqrt [3]{x^3-\sqrt {x^6-e^{6 c_1}}}\right \},\left \{y(x)\to (-1)^{2/3} \sqrt [3]{x^3-\sqrt {x^6-e^{6 c_1}}}\right \},\left \{y(x)\to \sqrt [3]{x^3+\sqrt {x^6-e^{6 c_1}}}\right \},\left \{y(x)\to -\sqrt [3]{-1} \sqrt [3]{x^3+\sqrt {x^6-e^{6 c_1}}}\right \},\left \{y(x)\to (-1)^{2/3} \sqrt [3]{x^3+\sqrt {x^6-e^{6 c_1}}}\right \}\right \}\] Maple : cpu = 0.263 (sec), leaf count = 231

\[\left \{y \left (x \right ) = \frac {x}{\left (-c_{1} \left (c_{1} x^{3}-\sqrt {c_{1}^{2} x^{6}+1}\right ) x^{3}\right )^{\frac {1}{3}}}, y \left (x \right ) = \frac {x}{\left (-c_{1} \left (c_{1} x^{3}+\sqrt {c_{1}^{2} x^{6}+1}\right ) x^{3}\right )^{\frac {1}{3}}}, y \left (x \right ) = \frac {4 x}{\left (1+i \sqrt {3}\right )^{2} \left (-c_{1} \left (c_{1} x^{3}-\sqrt {c_{1}^{2} x^{6}+1}\right ) x^{3}\right )^{\frac {1}{3}}}, y \left (x \right ) = \frac {4 x}{\left (1+i \sqrt {3}\right )^{2} \left (-c_{1} \left (c_{1} x^{3}+\sqrt {c_{1}^{2} x^{6}+1}\right ) x^{3}\right )^{\frac {1}{3}}}, y \left (x \right ) = \frac {4 x}{\left (i \sqrt {3}-1\right )^{2} \left (-c_{1} \left (c_{1} x^{3}-\sqrt {c_{1}^{2} x^{6}+1}\right ) x^{3}\right )^{\frac {1}{3}}}, y \left (x \right ) = \frac {4 x}{\left (i \sqrt {3}-1\right )^{2} \left (-c_{1} \left (c_{1} x^{3}+\sqrt {c_{1}^{2} x^{6}+1}\right ) x^{3}\right )^{\frac {1}{3}}}\right \}\]