3.504   ODE No. 504

$$\boxed{{\displaystyle x{\left(y\left(x\right)\right)}^2{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2-({\left(y\left(x\right)\right)}^3+x^3-a)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+x^{2}y\left(x\right)=0}}$$

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

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

Maple: cpu = 1.201 (sec), leaf count = 303 $$\{{\int }_{\mathit{\_}\mathit{b}}^{y\left(x\right)}{\mathit{\_}\mathit{a}}^2\frac{1}{\sqrt{{\mathit{\_}\mathit{a}}^6+(-2x^3-2a){\mathit{\_}\mathit{a}}^3+{(-x^3+a)}^2}}\mathrm{d}\mathit{\_}\mathit{a}-\frac{\ln \left(x\right)}{2}-\mathit{\_}\mathit{C}\mathit{1}=0,{\int }_{\mathit{\_}\mathit{b}}^{y\left(x\right)}{\mathit{\_}\mathit{a}}^2\frac{1}{\sqrt{{\mathit{\_}\mathit{a}}^6+(-2x^3-2a){\mathit{\_}\mathit{a}}^3+{(-x^3+a)}^2}}\mathrm{d}\mathit{\_}\mathit{a}+\frac{\ln \left(x\right)}{2}-\mathit{\_}\mathit{C}\mathit{1}=0,y\left(x\right)=\sqrt[3]{x^3+a-2x\sqrt{ax}},y\left(x\right)=\sqrt[3]{x^3+a+2x\sqrt{ax}},y\left(x\right)=-\frac{1}{2}\sqrt[3]{x^3+a-2x\sqrt{ax}}-\frac{i}{2}\sqrt{3}\sqrt[3]{x^3+a-2x\sqrt{ax}},y\left(x\right)=-\frac{1}{2}\sqrt[3]{x^3+a-2x\sqrt{ax}}+\frac{i}{2}\sqrt{3}\sqrt[3]{x^3+a-2x\sqrt{ax}},y\left(x\right)=-\frac{1}{2}\sqrt[3]{x^3+a+2x\sqrt{ax}}-\frac{i}{2}\sqrt{3}\sqrt[3]{x^3+a+2x\sqrt{ax}},y\left(x\right)=-\frac{1}{2}\sqrt[3]{x^3+a+2x\sqrt{ax}}+\frac{i}{2}\sqrt{3}\sqrt[3]{x^3+a+2x\sqrt{ax}}\}$$