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 = 0.182895 (sec), leaf count = 34

DSolve[-4*x^2 - 6*x*y[x]^5*Derivative[1][y][x] + 9*(-1 + x^2)*y[x]^4*Derivative[1][y][x]^2 == 0,y[x],x]

\[\left \{y(x)\to -\frac {\sqrt [3]{-\frac {1}{2}} \sqrt [3]{-4 x^2+4+c_1{}^2}}{\sqrt [3]{c_1}}\right \}\]

✓ Maple : cpu = 0.566 (sec), leaf count = 212

dsolve(9*y(x)^4*(x^2-1)*diff(y(x),x)^2-6*x*y(x)^5*diff(y(x),x)-4*x^2=0,y(x))

\[y \left (x \right ) = \left (-4 x^{2}+4\right )^{{1}/{6}}\]