2.305   ODE No. 305

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

$$x^2+(y(x{)}^3-3x)y^{\prime }(x)-3y(x)=0$$ ✓ Mathematica : cpu = 0.0995662 (sec), leaf count = 1277

$$\{\{y(x)\to -\frac{1}{2}\sqrt{\frac{16\sqrt[3]{2}(x^3+3c_1)}{\sqrt[3]{104976x^2-\sqrt{11019960576x^4-4(144x^3+432c_1){}^3}}}+\frac{\sqrt[3]{104976x^2-\sqrt{11019960576x^4-4(144x^3+432c_1){}^3}}}{9\sqrt[3]{2}}}-\frac{1}{2}\sqrt{-\frac{24x}{\sqrt{\frac{16\sqrt[3]{2}(x^3+3c_1)}{\sqrt[3]{104976x^2-\sqrt{11019960576x^4-4(144x^3+432c_1){}^3}}}+\frac{\sqrt[3]{104976x^2-\sqrt{11019960576x^4-4(144x^3+432c_1){}^3}}}{9\sqrt[3]{2}}}}-\frac{\sqrt[3]{104976x^2-\sqrt{11019960576x^4-4(144x^3+432c_1){}^3}}}{9\sqrt[3]{2}}-\frac{16\sqrt[3]{2}(x^3+3c_1)}{\sqrt[3]{104976x^2-\sqrt{11019960576x^4-4(144x^3+432c_1){}^3}}}}\},\{y(x)\to \frac{1}{2}\sqrt{-\frac{24x}{\sqrt{\frac{16\sqrt[3]{2}(x^3+3c_1)}{\sqrt[3]{104976x^2-\sqrt{11019960576x^4-4(144x^3+432c_1){}^3}}}+\frac{\sqrt[3]{104976x^2-\sqrt{11019960576x^4-4(144x^3+432c_1){}^3}}}{9\sqrt[3]{2}}}}-\frac{\sqrt[3]{104976x^2-\sqrt{11019960576x^4-4(144x^3+432c_1){}^3}}}{9\sqrt[3]{2}}-\frac{16\sqrt[3]{2}(x^3+3c_1)}{\sqrt[3]{104976x^2-\sqrt{11019960576x^4-4(144x^3+432c_1){}^3}}}}-\frac{1}{2}\sqrt{\frac{16\sqrt[3]{2}(x^3+3c_1)}{\sqrt[3]{104976x^2-\sqrt{11019960576x^4-4(144x^3+432c_1){}^3}}}+\frac{\sqrt[3]{104976x^2-\sqrt{11019960576x^4-4(144x^3+432c_1){}^3}}}{9\sqrt[3]{2}}}\},\{y(x)\to \frac{1}{2}\sqrt{\frac{16\sqrt[3]{2}(x^3+3c_1)}{\sqrt[3]{104976x^2-\sqrt{11019960576x^4-4(144x^3+432c_1){}^3}}}+\frac{\sqrt[3]{104976x^2-\sqrt{11019960576x^4-4(144x^3+432c_1){}^3}}}{9\sqrt[3]{2}}}-\frac{1}{2}\sqrt{\frac{24x}{\sqrt{\frac{16\sqrt[3]{2}(x^3+3c_1)}{\sqrt[3]{104976x^2-\sqrt{11019960576x^4-4(144x^3+432c_1){}^3}}}+\frac{\sqrt[3]{104976x^2-\sqrt{11019960576x^4-4(144x^3+432c_1){}^3}}}{9\sqrt[3]{2}}}}-\frac{\sqrt[3]{104976x^2-\sqrt{11019960576x^4-4(144x^3+432c_1){}^3}}}{9\sqrt[3]{2}}-\frac{16\sqrt[3]{2}(x^3+3c_1)}{\sqrt[3]{104976x^2-\sqrt{11019960576x^4-4(144x^3+432c_1){}^3}}}}\},\{y(x)\to \frac{1}{2}\sqrt{\frac{16\sqrt[3]{2}(x^3+3c_1)}{\sqrt[3]{104976x^2-\sqrt{11019960576x^4-4(144x^3+432c_1){}^3}}}+\frac{\sqrt[3]{104976x^2-\sqrt{11019960576x^4-4(144x^3+432c_1){}^3}}}{9\sqrt[3]{2}}}+\frac{1}{2}\sqrt{\frac{24x}{\sqrt{\frac{16\sqrt[3]{2}(x^3+3c_1)}{\sqrt[3]{104976x^2-\sqrt{11019960576x^4-4(144x^3+432c_1){}^3}}}+\frac{\sqrt[3]{104976x^2-\sqrt{11019960576x^4-4(144x^3+432c_1){}^3}}}{9\sqrt[3]{2}}}}-\frac{\sqrt[3]{104976x^2-\sqrt{11019960576x^4-4(144x^3+432c_1){}^3}}}{9\sqrt[3]{2}}-\frac{16\sqrt[3]{2}(x^3+3c_1)}{\sqrt[3]{104976x^2-\sqrt{11019960576x^4-4(144x^3+432c_1){}^3}}}}\}\}$$

✓ Maple : cpu = 0.024 (sec), leaf count = 21

$$\{\frac{x^3}{3}-3xy\left(x\right)+\frac{{\left(y\left(x\right)\right)}^4}{4}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$