2.1808   ODE No. 1808

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

$$b\sqrt{(1-y(x{)}^2)(1-a^{2}y(x{)}^2)}{y}^{\prime }(x{)}^2+(y(x{)}^2-1)(a^{2}y(x{)}^2-1)y^{″}(x)+y(x)(-2a^{2}y(x{)}^2+a^2+1)y^{\prime }(x{)}^2=0$$ ✓ Mathematica : cpu = 103.91 (sec), leaf count = 172

$$\text{Solve}[\log (x)-b(\frac{\log (b{c}_1\sqrt{1-y(x{)}^2}\sqrt{1-a^{2}y(x{)}^2}+\sqrt{y(x{)}^2-1}\sqrt{a^{2}y(x{)}^2-1}\exp \left(\frac{b\sqrt{1-y(x{)}^2}\sqrt{1-a^{2}y(x{)}^2}F({\sin }^{-1}(y(x))|a^2)}{\sqrt{y(x{)}^2-1}\sqrt{a^{2}y(x{)}^2-1}}\right))}{b}-\frac{\log (1-a^{2}y(x{)}^2)}{2b}-\frac{\log (1-y(x{)}^2)}{2b})=c_2,y(x)]$$

✓ Maple : cpu = 1.13 (sec), leaf count = 72

$$\{{\int }^{y\left(x\right)}{\mathrm{e}}^{\int \frac{1}{({\mathit{\_}\mathit{b}}^2-1)({\mathit{\_}\mathit{b}}^2{a}^2-1)}(-2a^2{\mathit{\_}\mathit{b}}^3+\mathit{\_}\mathit{b}{a}^2+b\sqrt{({\mathit{\_}\mathit{b}}^2-1)({\mathit{\_}\mathit{b}}^2{a}^2-1)}+\mathit{\_}\mathit{b})\mathrm{d}\mathit{\_}\mathit{b}}d\mathit{\_}\mathit{b}-\mathit{\_}\mathit{C}\mathit{1}x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$