2.1833   ODE No. 1833

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

$$y^{″}(x{)}^2(a^{2}y(x{)}^2-b^2)+y^{\prime }(x{)}^2(a^2{y}^{\prime }(x{)}^2-1)-2a^{2}y(x)y^{\prime }(x{)}^2{y}^{″}(x)=0$$ ✗ Mathematica : cpu = 300.107 (sec), leaf count = 0 , timed out

$Aborted

✓ Maple : cpu = 4.19 (sec), leaf count = 145

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1},y\left(x\right)=b({\mathrm{e}}^{\frac{\mathit{\_}\mathit{C}\mathit{2}+x}{b}\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^2-1}}-\mathit{\_}\mathit{C}\mathit{1})\frac{1}{\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^2-1}},y\left(x\right)=\frac{b}{a}\tan \left(\frac{\mathit{\_}\mathit{C}\mathit{1}-x}{ab}\sqrt{a^2}\right)\frac{1}{\sqrt{{(\tan \left(\frac{\mathit{\_}\mathit{C}\mathit{1}-x}{ab}\sqrt{a^2}\right))}^2+1}},y\left(x\right)=-\frac{b}{a}\tan \left(\frac{\mathit{\_}\mathit{C}\mathit{1}-x}{ab}\sqrt{a^2}\right)\frac{1}{\sqrt{{(\tan \left(\frac{\mathit{\_}\mathit{C}\mathit{1}-x}{ab}\sqrt{a^2}\right))}^2+1}}\}$$