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 = 0.1583 (sec), leaf count = 402

$$\{\{y(x)\to -\frac{33x^2}{22^{2/3}\sqrt[3]{54x^3+\sqrt{3881196x^6+(54x^3+432e^{3c_1}){}^2}+432e^{3c_1}}}+\frac{\sqrt[3]{54x^3+\sqrt{3881196x^6+(54x^3+432e^{3c_1}){}^2}+432e^{3c_1}}}{12\sqrt[3]{2}}-\frac{x}{4}\},\{y(x)\to \frac{33(1+i\sqrt{3})x^2}{42^{2/3}\sqrt[3]{54x^3+\sqrt{3881196x^6+(54x^3+432e^{3c_1}){}^2}+432e^{3c_1}}}-\frac{(1-i\sqrt{3})\sqrt[3]{54x^3+\sqrt{3881196x^6+(54x^3+432e^{3c_1}){}^2}+432e^{3c_1}}}{24\sqrt[3]{2}}-\frac{x}{4}\},\{y(x)\to \frac{33(1-i\sqrt{3})x^2}{42^{2/3}\sqrt[3]{54x^3+\sqrt{3881196x^6+(54x^3+432e^{3c_1}){}^2}+432e^{3c_1}}}-\frac{(1+i\sqrt{3})\sqrt[3]{54x^3+\sqrt{3881196x^6+(54x^3+432e^{3c_1}){}^2}+432e^{3c_1}}}{24\sqrt[3]{2}}-\frac{x}{4}\}\}$$ ✓ Maple : cpu = 0.064 (sec), leaf count = 432

$$\{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}{8\mathit{\_}\mathit{C}\mathit{1}}(2\mathit{\_}\mathit{C}\mathit{1}x\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}}+(11i{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+i{(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{2}{3}})\sqrt{3}-11{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+{(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{2}{3}})\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}{8\mathit{\_}\mathit{C}\mathit{1}}(11i\sqrt{3}{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+i{(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{2}{3}}\sqrt{3}+11{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2-2\mathit{\_}\mathit{C}\mathit{1}x\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}}-{(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{2}{3}})\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}}}\}$$