2.294   ODE No. 294

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

$$x(-a+x^2+y(x{)}^2)y^{\prime }(x)-y(x)(a+x^2+y(x{)}^2)=0$$ ✓ Mathematica : cpu = 0.226574 (sec), leaf count = 71

$$\{\{y(x)\to \frac{1}{2}(c_{1}x-\sqrt{-4a+4x^2+c_1{}^2{x}^2})\},\{y(x)\to \frac{1}{2}(\sqrt{-4a+4x^2+c_1{}^2{x}^2}+c_{1}x)\}\}$$ ✓ Maple : cpu = 0.068 (sec), leaf count = 112

$$\{{({\left(y\left(x\right)\right)}^{-2}-{(-x^2+a)}^{-1})}^{-1}=-x\sqrt{x^2-a}\frac{1}{\sqrt{\mathit{\_}\mathit{C}\mathit{1}+4\frac{a}{x^2-a}}}+\frac{x^2}{2}-\frac{a}{2},{({\left(y\left(x\right)\right)}^{-2}-{(-x^2+a)}^{-1})}^{-1}=x\sqrt{x^2-a}\frac{1}{\sqrt{\mathit{\_}\mathit{C}\mathit{1}+4\frac{a}{x^2-a}}}+\frac{x^2}{2}-\frac{a}{2}\}$$