#### 2.509   ODE No. 509

$9 \left (x^2-1\right ) y(x)^4 y'(x)^2-4 x^2-6 x y(x)^5 y'(x)=0$ Mathematica : cpu = 0.276089 (sec), leaf count = 34

$\left \{y(x)\to -\frac {\sqrt [3]{-\frac {1}{2}} \sqrt [3]{c_1{}^2-4 x^2+4}}{\sqrt [3]{c_1}}\right \}$ Maple : cpu = 1.148 (sec), leaf count = 212

$\left \{ y \left ( x \right ) =\sqrt [6]{-4\,{x}^{2}+4},y \left ( x \right ) =-\sqrt [6]{-4\,{x}^{2}+4},y \left ( x \right ) =-{\frac {i\sqrt {3}-1}{2}\sqrt [6]{-4\,{x}^{2}+4}},y \left ( x \right ) ={\frac {i\sqrt {3}-1}{2}\sqrt [6]{-4\,{x}^{2}+4}},y \left ( x \right ) =-{\frac {i\sqrt {3}+1}{2}\sqrt [6]{-4\,{x}^{2}+4}},y \left ( x \right ) ={\frac {i\sqrt {3}+1}{2}\sqrt [6]{-4\,{x}^{2}+4}},y \left ( x \right ) ={\frac {\sqrt [3]{4}}{2\,{\it \_C1}}\sqrt [3]{ \left ( -4\,{{\it \_C1}}^{2}+{x}^{2}-1 \right ) {{\it \_C1}}^{2}}},y \left ( x \right ) ={\frac {\sqrt [3]{4} \left ( i\sqrt {3}-1 \right ) }{4\,{\it \_C1}}\sqrt [3]{ \left ( -4\,{{\it \_C1}}^{2}+{x}^{2}-1 \right ) {{\it \_C1}}^{2}}},y \left ( x \right ) =-{\frac {\sqrt [3]{4} \left ( i\sqrt {3}+1 \right ) }{4\,{\it \_C1}}\sqrt [3]{ \left ( -4\,{{\it \_C1}}^{2}+{x}^{2}-1 \right ) {{\it \_C1}}^{2}}} \right \}$