3.307   ODE No. 307

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

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

Mathematica: cpu = 0.024003 (sec), leaf count = 149 $$\{\{y(x)\to -\sqrt{-\sqrt{a^2+4a{x}^2+4c_1}-a-x^2}\},\{y(x)\to \sqrt{-\sqrt{a^2+4a{x}^2+4c_1}-a-x^2}\},\{y(x)\to -\sqrt{\sqrt{a^2+4a{x}^2+4c_1}-a-x^2}\},\{y(x)\to \sqrt{\sqrt{a^2+4a{x}^2+4c_1}-a-x^2}\}\}$$

Maple: cpu = 0.046 (sec), leaf count = 125 $$\{y\left(x\right)=\sqrt{-x^2-a-\sqrt{4a{x}^2+a^2-4\mathit{\_}\mathit{C}\mathit{1}}},y\left(x\right)=\sqrt{-x^2-a+\sqrt{4a{x}^2+a^2-4\mathit{\_}\mathit{C}\mathit{1}}},y\left(x\right)=-\sqrt{-x^2-a-\sqrt{4a{x}^2+a^2-4\mathit{\_}\mathit{C}\mathit{1}}},y\left(x\right)=-\sqrt{-x^2-a+\sqrt{4a{x}^2+a^2-4\mathit{\_}\mathit{C}\mathit{1}}}\}$$