3.294   ODE No. 294

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

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

Mathematica: cpu = 0.040005 (sec), leaf count = 71 $$\{\{y(x)\to \frac{1}{2}(c_{1}x-\sqrt{-4a+c_1^2{x}^2+4x^2})\},\{y(x)\to \frac{1}{2}(\sqrt{-4a+c_1^2{x}^2+4x^2}+c_{1}x)\}\}$$

Maple: cpu = 0.078 (sec), leaf count = 112 $$\{{({\left(y\left(x\right)\right)}^{-2}-{(-x^2+a)}^{-1})}^{-1}=-x\sqrt{x^2-a}\frac{1}{\sqrt{\mathit{\_}\mathit{C}\mathit{1}+4\frac{a}{x^2-a}}}+\frac{x^2}{2}-\frac{a}{2},{({\left(y\left(x\right)\right)}^{-2}-{(-x^2+a)}^{-1})}^{-1}=x\sqrt{x^2-a}\frac{1}{\sqrt{\mathit{\_}\mathit{C}\mathit{1}+4\frac{a}{x^2-a}}}+\frac{x^2}{2}-\frac{a}{2}\}$$