8.243   ODE No. 1833

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

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

Mathematica: cpu = 0 (sec), leaf count = 0 $$\text{Hanged}$$

Maple: cpu = 2.465 (sec), leaf count = 145 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1},y\left(x\right)=b({\mathrm{e}}^{\frac{\mathit{\_}\mathit{C}\mathit{2}+x}{b}\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^2-1}}-\mathit{\_}\mathit{C}\mathit{1})\frac{1}{\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^2-1}},y\left(x\right)=\frac{b}{a}\tan \left(\frac{\mathit{\_}\mathit{C}\mathit{1}-x}{ab}\sqrt{a^2}\right)\frac{1}{\sqrt{{(\tan \left(\frac{\mathit{\_}\mathit{C}\mathit{1}-x}{ab}\sqrt{a^2}\right))}^2+1}},y\left(x\right)=-\frac{b}{a}\tan \left(\frac{\mathit{\_}\mathit{C}\mathit{1}-x}{ab}\sqrt{a^2}\right)\frac{1}{\sqrt{{(\tan \left(\frac{\mathit{\_}\mathit{C}\mathit{1}-x}{ab}\sqrt{a^2}\right))}^2+1}}\}$$