8.218   ODE No. 1808

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

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

Mathematica: cpu = 103.724671 (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 = 0.110 (sec), leaf count = 72 $$\{{\int }^{y\left(x\right)}{\mathrm{e}}^{\int \frac{1}{({\mathit{\_}\mathit{b}}^2-1)({\mathit{\_}\mathit{b}}^2{a}^2-1)}(-2{\mathit{\_}\mathit{b}}^3{a}^2+\mathit{\_}\mathit{b}{a}^2+b\sqrt{({\mathit{\_}\mathit{b}}^2-1)({\mathit{\_}\mathit{b}}^2{a}^2-1)}+\mathit{\_}\mathit{b})\mathrm{d}\mathit{\_}\mathit{b}}d\mathit{\_}\mathit{b}-\mathit{\_}\mathit{C}\mathit{1}x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$