3.509   ODE No. 509

$$\boxed{{\displaystyle 9{\left(y\left(x\right)\right)}^4(x^2-1){\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2-6x{\left(y\left(x\right)\right)}^5\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-4x^2=0}}$$

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

Mathematica: cpu = 0 (sec), leaf count = 0 $$\text{Hanged}$$

Maple: cpu = 1.622 (sec), leaf count = 245 $$\{y\left(x\right)=\sqrt[6]{-4x^2+4},y\left(x\right)=(-\frac{1}{2}-\frac{i}{2}\sqrt{3})\sqrt[6]{-4x^2+4},y\left(x\right)=(-\frac{1}{2}+\frac{i}{2}\sqrt{3})\sqrt[6]{-4x^2+4},y\left(x\right)=(\frac{1}{2}-\frac{i}{2}\sqrt{3})\sqrt[6]{-4x^2+4},y\left(x\right)=(\frac{1}{2}+\frac{i}{2}\sqrt{3})\sqrt[6]{-4x^2+4},y\left(x\right)=-\sqrt[6]{-4x^2+4},y\left(x\right)=\frac{1}{2\mathit{\_}\mathit{C}\mathit{1}}\sqrt[3]{(-16{\mathit{\_}\mathit{C}\mathit{1}}^2+4x^2-4){\mathit{\_}\mathit{C}\mathit{1}}^2},y\left(x\right)=-\frac{1}{4\mathit{\_}\mathit{C}\mathit{1}}\sqrt[3]{(-16{\mathit{\_}\mathit{C}\mathit{1}}^2+4x^2-4){\mathit{\_}\mathit{C}\mathit{1}}^2}-\frac{\frac{i}{4}\sqrt{3}}{\mathit{\_}\mathit{C}\mathit{1}}\sqrt[3]{(-16{\mathit{\_}\mathit{C}\mathit{1}}^2+4x^2-4){\mathit{\_}\mathit{C}\mathit{1}}^2},y\left(x\right)=-\frac{1}{4\mathit{\_}\mathit{C}\mathit{1}}\sqrt[3]{(-16{\mathit{\_}\mathit{C}\mathit{1}}^2+4x^2-4){\mathit{\_}\mathit{C}\mathit{1}}^2}+\frac{\frac{i}{4}\sqrt{3}}{\mathit{\_}\mathit{C}\mathit{1}}\sqrt[3]{(-16{\mathit{\_}\mathit{C}\mathit{1}}^2+4x^2-4){\mathit{\_}\mathit{C}\mathit{1}}^2}\}$$