2.178   ODE No. 178

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

$$2(x^2-1)x{y}^{\prime }(x)+2(x^2-1)y(x{)}^2-(3x^2-5)y(x)+x^2-3=0$$ ✓ Mathematica : cpu = 0.144119 (sec), leaf count = 49

$$\left\{\{y(x)\to 1+\frac{\sqrt{x}}{\sqrt{1-x^2}(2\sqrt{x}{}_2{F}_1(\frac{1}{4},\frac{1}{2};\frac{5}{4};x^2)+c_1)}\}\right\}$$ ✓ Maple : cpu = 0.079 (sec), leaf count = 61

$$\{y\left(x\right)=1-2\frac{\sqrt{x}}{\sqrt{x-1}\sqrt{1+x}}{(\mathit{\_}\mathit{C}\mathit{1}-2\frac{\mathit{E}\mathit{l}\mathit{l}\mathit{i}\mathit{p}\mathit{t}\mathit{i}\mathit{c}\mathit{F}(\sqrt{1+x},1/2\sqrt{2})\sqrt{-x}\sqrt{2}\sqrt{1-x}}{\sqrt{x-1}\sqrt{x}})}^{-1}\}$$