3.178   ODE No. 178

$$\boxed{{\displaystyle 2x(x^2-1)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+2(x^2-1){\left(y\left(x\right)\right)}^2-(3x^2-5)y\left(x\right)+x^2-3=0}}$$

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

Mathematica: cpu = 0.068009 (sec), leaf count = 62 $$\left\{\{y(x)\to \frac{\sqrt{x}}{\sqrt{1-x^2}(c_1-\frac{2\sqrt{1-\frac{1}{x^2}}xF({\sin }^{-1}\left(\frac{1}{\sqrt{x}}\right)|-1)}{\sqrt{1-x^2}})}+1\}\right\}$$

Maple: cpu = 0.110 (sec), leaf count = 63 $$\{y\left(x\right)=1-2\frac{\sqrt{x}}{\sqrt{x-1}\sqrt{1+x}}{(\mathit{\_}\mathit{C}\mathit{1}-2\frac{\mathit{E}\mathit{l}\mathit{l}\mathit{i}\mathit{p}\mathit{t}\mathit{i}\mathit{c}\mathit{F}(\sqrt{1+x},1/2\sqrt{2})\sqrt{-x}\sqrt{-2x+2}\sqrt{2}}{\sqrt{2x-2}\sqrt{x}})}^{-1}\}$$