2.274   ODE No. 274

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

$$(a+x^2+y(x{)}^2)y^{\prime }(x)+b+x^2+2xy(x)=0$$ ✓ Mathematica : cpu = 0.165573 (sec), leaf count = 411

$$\{\{y(x)\to \frac{\sqrt[3]{\sqrt{2916{(a+x^2)}^3+(-81bx-27x^3+81c_1){}^2}-81bx-27x^3+81c_1}}{3\sqrt[3]{2}}-\frac{3\sqrt[3]{2}(a+x^2)}{\sqrt[3]{\sqrt{2916{(a+x^2)}^3+(-81bx-27x^3+81c_1){}^2}-81bx-27x^3+81c_1}}\},\{y(x)\to \frac{3(1+i\sqrt{3})(a+x^2)}{2^{2/3}\sqrt[3]{\sqrt{2916{(a+x^2)}^3+(-81bx-27x^3+81c_1){}^2}-81bx-27x^3+81c_1}}-\frac{(1-i\sqrt{3})\sqrt[3]{\sqrt{2916{(a+x^2)}^3+(-81bx-27x^3+81c_1){}^2}-81bx-27x^3+81c_1}}{6\sqrt[3]{2}}\},\{y(x)\to \frac{3(1-i\sqrt{3})(a+x^2)}{2^{2/3}\sqrt[3]{\sqrt{2916{(a+x^2)}^3+(-81bx-27x^3+81c_1){}^2}-81bx-27x^3+81c_1}}-\frac{(1+i\sqrt{3})\sqrt[3]{\sqrt{2916{(a+x^2)}^3+(-81bx-27x^3+81c_1){}^2}-81bx-27x^3+81c_1}}{6\sqrt[3]{2}}\}\}$$ ✓ Maple : cpu = 0.031 (sec), leaf count = 657

$$\{y\left(x\right)=\frac{1}{2}({(-4x^3-12bx-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{5x^6+(12a+6b)x^4+6x^3\mathit{\_}\mathit{C}\mathit{1}+(12a^2+9b^2)x^2+18bx\mathit{\_}\mathit{C}\mathit{1}+4a^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2})}^{\frac{2}{3}}-4x^2-4a)\frac{1}{\sqrt[3]{-4x^3-12bx-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{5x^6+(12a+6b)x^4+6x^3\mathit{\_}\mathit{C}\mathit{1}+(12a^2+9b^2)x^2+18bx\mathit{\_}\mathit{C}\mathit{1}+4a^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}},y\left(x\right)=\frac{1}{4}((i{(-4x^3-12bx-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{5x^6+(12a+6b)x^4+6x^3\mathit{\_}\mathit{C}\mathit{1}+(12a^2+9b^2)x^2+18bx\mathit{\_}\mathit{C}\mathit{1}+4a^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2})}^{\frac{2}{3}}+4i{x}^2+4ia)\sqrt{3}-{(-4x^3-12bx-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{5x^6+(12a+6b)x^4+6x^3\mathit{\_}\mathit{C}\mathit{1}+(12a^2+9b^2)x^2+18bx\mathit{\_}\mathit{C}\mathit{1}+4a^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2})}^{\frac{2}{3}}+4x^2+4a)\frac{1}{\sqrt[3]{-4x^3-12bx-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{5x^6+(12a+6b)x^4+6x^3\mathit{\_}\mathit{C}\mathit{1}+(12a^2+9b^2)x^2+18bx\mathit{\_}\mathit{C}\mathit{1}+4a^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}},y\left(x\right)=-\frac{1}{4}((i{(-4x^3-12bx-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{5x^6+(12a+6b)x^4+6x^3\mathit{\_}\mathit{C}\mathit{1}+(12a^2+9b^2)x^2+18bx\mathit{\_}\mathit{C}\mathit{1}+4a^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2})}^{\frac{2}{3}}+4i{x}^2+4ia)\sqrt{3}+{(-4x^3-12bx-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{5x^6+(12a+6b)x^4+6x^3\mathit{\_}\mathit{C}\mathit{1}+(12a^2+9b^2)x^2+18bx\mathit{\_}\mathit{C}\mathit{1}+4a^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2})}^{\frac{2}{3}}-4x^2-4a)\frac{1}{\sqrt[3]{-4x^3-12bx-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{5x^6+(12a+6b)x^4+6x^3\mathit{\_}\mathit{C}\mathit{1}+(12a^2+9b^2)x^2+18bx\mathit{\_}\mathit{C}\mathit{1}+4a^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}}\}$$