2.285   ODE No. 285

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

$$(3x^2+2xy(x)+4y(x{)}^2)y^{\prime }(x)+2x^2+6xy(x)+y(x{)}^2=0$$ ✓ Mathematica : cpu = 0.060572 (sec), leaf count = 402

$$\{\{y(x)\to \frac{\sqrt[3]{\sqrt{(432e^{3c_1}+54x^3){}^2+3881196x^6}+432e^{3c_1}+54x^3}}{12\sqrt[3]{2}}-\frac{33x^2}{22^{2/3}\sqrt[3]{\sqrt{(432e^{3c_1}+54x^3){}^2+3881196x^6}+432e^{3c_1}+54x^3}}-\frac{x}{4}\},\{y(x)\to -\frac{(1-i\sqrt{3})\sqrt[3]{\sqrt{(432e^{3c_1}+54x^3){}^2+3881196x^6}+432e^{3c_1}+54x^3}}{24\sqrt[3]{2}}+\frac{33(1+i\sqrt{3})x^2}{42^{2/3}\sqrt[3]{\sqrt{(432e^{3c_1}+54x^3){}^2+3881196x^6}+432e^{3c_1}+54x^3}}-\frac{x}{4}\},\{y(x)\to -\frac{(1+i\sqrt{3})\sqrt[3]{\sqrt{(432e^{3c_1}+54x^3){}^2+3881196x^6}+432e^{3c_1}+54x^3}}{24\sqrt[3]{2}}+\frac{33(1-i\sqrt{3})x^2}{42^{2/3}\sqrt[3]{\sqrt{(432e^{3c_1}+54x^3){}^2+3881196x^6}+432e^{3c_1}+54x^3}}-\frac{x}{4}\}\}$$

✓ Maple : cpu = 0.159 (sec), leaf count = 431

$$\{y\left(x\right)=\frac{1}{\mathit{\_}\mathit{C}\mathit{1}}(\frac{1}{4}\sqrt[3]{x^3{\mathit{\_}\mathit{C}\mathit{1}}^3+8+2\sqrt{333{\mathit{\_}\mathit{C}\mathit{1}}^6{x}^6+4x^3{\mathit{\_}\mathit{C}\mathit{1}}^3+16}}-\frac{11{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2}{4}\frac{1}{\sqrt[3]{x^3{\mathit{\_}\mathit{C}\mathit{1}}^3+8+2\sqrt{333{\mathit{\_}\mathit{C}\mathit{1}}^6{x}^6+4x^3{\mathit{\_}\mathit{C}\mathit{1}}^3+16}}}-\frac{\mathit{\_}\mathit{C}\mathit{1}x}{4}),y\left(x\right)=\frac{1}{\mathit{\_}\mathit{C}\mathit{1}}(-\frac{1}{8}\sqrt[3]{x^3{\mathit{\_}\mathit{C}\mathit{1}}^3+8+2\sqrt{333{\mathit{\_}\mathit{C}\mathit{1}}^6{x}^6+4x^3{\mathit{\_}\mathit{C}\mathit{1}}^3+16}}+\frac{11{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2}{8}\frac{1}{\sqrt[3]{x^3{\mathit{\_}\mathit{C}\mathit{1}}^3+8+2\sqrt{333{\mathit{\_}\mathit{C}\mathit{1}}^6{x}^6+4x^3{\mathit{\_}\mathit{C}\mathit{1}}^3+16}}}-\frac{\mathit{\_}\mathit{C}\mathit{1}x}{4}-\frac{i}{2}\sqrt{3}(\frac{1}{4}\sqrt[3]{x^3{\mathit{\_}\mathit{C}\mathit{1}}^3+8+2\sqrt{333{\mathit{\_}\mathit{C}\mathit{1}}^6{x}^6+4x^3{\mathit{\_}\mathit{C}\mathit{1}}^3+16}}+\frac{11{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2}{4}\frac{1}{\sqrt[3]{x^3{\mathit{\_}\mathit{C}\mathit{1}}^3+8+2\sqrt{333{\mathit{\_}\mathit{C}\mathit{1}}^6{x}^6+4x^3{\mathit{\_}\mathit{C}\mathit{1}}^3+16}}})),y\left(x\right)=\frac{1}{\mathit{\_}\mathit{C}\mathit{1}}(-\frac{1}{8}\sqrt[3]{x^3{\mathit{\_}\mathit{C}\mathit{1}}^3+8+2\sqrt{333{\mathit{\_}\mathit{C}\mathit{1}}^6{x}^6+4x^3{\mathit{\_}\mathit{C}\mathit{1}}^3+16}}+\frac{11{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2}{8}\frac{1}{\sqrt[3]{x^3{\mathit{\_}\mathit{C}\mathit{1}}^3+8+2\sqrt{333{\mathit{\_}\mathit{C}\mathit{1}}^6{x}^6+4x^3{\mathit{\_}\mathit{C}\mathit{1}}^3+16}}}-\frac{\mathit{\_}\mathit{C}\mathit{1}x}{4}+\frac{i}{2}\sqrt{3}(\frac{1}{4}\sqrt[3]{x^3{\mathit{\_}\mathit{C}\mathit{1}}^3+8+2\sqrt{333{\mathit{\_}\mathit{C}\mathit{1}}^6{x}^6+4x^3{\mathit{\_}\mathit{C}\mathit{1}}^3+16}}+\frac{11{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2}{4}\frac{1}{\sqrt[3]{x^3{\mathit{\_}\mathit{C}\mathit{1}}^3+8+2\sqrt{333{\mathit{\_}\mathit{C}\mathit{1}}^6{x}^6+4x^3{\mathit{\_}\mathit{C}\mathit{1}}^3+16}}}))\}$$