2.509   ODE No. 509

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

\[ 9 \left (x^2-1\right ) y(x)^4 y'(x)^2-4 x^2-6 x y(x)^5 y'(x)=0 \] Mathematica : cpu = 0.332651 (sec), leaf count = 34

\[\left \{y(x)\to -\frac {\sqrt [3]{-\frac {1}{2}} \sqrt [3]{-4 x^2+4+c_1{}^2}}{\sqrt [3]{c_1}}\right \}\] Maple : cpu = 1.554 (sec), leaf count = 212

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