3.273   ODE No. 273

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

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

Mathematica: cpu = 0.014002 (sec), leaf count = 297 $$\{\{y(x)\to \frac{\sqrt[3]{\sqrt{2916{(a+x^2)}^3+6561c_1^2}+81c_1}}{3\sqrt[3]{2}}-\frac{3\sqrt[3]{2}(a+x^2)}{\sqrt[3]{\sqrt{2916{(a+x^2)}^3+6561c_1^2}+81c_1}}\},\{y(x)\to \frac{3(1+i\sqrt{3})(a+x^2)}{2^{2/3}\sqrt[3]{\sqrt{2916{(a+x^2)}^3+6561c_1^2}+81c_1}}-\frac{(1-i\sqrt{3})\sqrt[3]{\sqrt{2916{(a+x^2)}^3+6561c_1^2}+81c_1}}{6\sqrt[3]{2}}\},\{y(x)\to \frac{3(1-i\sqrt{3})(a+x^2)}{2^{2/3}\sqrt[3]{\sqrt{2916{(a+x^2)}^3+6561c_1^2}+81c_1}}-\frac{(1+i\sqrt{3})\sqrt[3]{\sqrt{2916{(a+x^2)}^3+6561c_1^2}+81c_1}}{6\sqrt[3]{2}}\}\}$$

Maple: cpu = 0.015 (sec), leaf count = 470 $$\{y\left(x\right)=\frac{1}{2}\sqrt[3]{-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{4x^6+12a{x}^4+12a^2{x}^2+4a^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}-2\frac{x^2+a}{\sqrt[3]{-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{4x^6+12a{x}^4+12a^2{x}^2+4a^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}},y\left(x\right)=-\frac{1}{4}\sqrt[3]{-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{4x^6+12a{x}^4+12a^2{x}^2+4a^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}+(x^2+a)\frac{1}{\sqrt[3]{-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{4x^6+12a{x}^4+12a^2{x}^2+4a^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}}-\frac{i}{2}\sqrt{3}(\frac{1}{2}\sqrt[3]{-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{4x^6+12a{x}^4+12a^2{x}^2+4a^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}+2\frac{x^2+a}{\sqrt[3]{-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{4x^6+12a{x}^4+12a^2{x}^2+4a^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}}),y\left(x\right)=-\frac{1}{4}\sqrt[3]{-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{4x^6+12a{x}^4+12a^2{x}^2+4a^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}+(x^2+a)\frac{1}{\sqrt[3]{-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{4x^6+12a{x}^4+12a^2{x}^2+4a^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}}+\frac{i}{2}\sqrt{3}(\frac{1}{2}\sqrt[3]{-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{4x^6+12a{x}^4+12a^2{x}^2+4a^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}+2\frac{x^2+a}{\sqrt[3]{-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{4x^6+12a{x}^4+12a^2{x}^2+4a^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}})\}$$