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 = 1.03828 (sec), leaf count = 124

$$\left\{\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{\exp (\frac{b\sqrt{1-K[1{]}^2}\sqrt{1-a^{2}K[1{]}^2}F({\sin }^{-1}(K[1])|a^2)}{\sqrt{(K[1{]}^2-1)(a^{2}K[1{]}^2-1)}}+\frac{1}{2}(-\log (1-K[1])-\log (K[1]+1)-\log (1-aK[1])-\log (aK[1]+1)))}{c_1}dK[1]\mathrm{\&}][c_2+x]\}\right\}$$ ✓ Maple : cpu = 0.105 (sec), leaf count = 72

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