3.68   ODE No. 68

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-\sqrt{\frac{a{\left(y\left(x\right)\right)}^4+b{\left(y\left(x\right)\right)}^2+1}{a{x}^4+b{x}^2+1}}=0}}$$

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

Mathematica: cpu = 1.108641 (sec), leaf count = 373 $$\left\{\{y(x)\to \text{InverseFunction}[-\frac{i\sqrt{\frac{2{\mathrm{\#}\text{1}}^{2}a+\sqrt{b^2-4a}+b}{\sqrt{b^2-4a}+b}}\sqrt{\frac{2{\mathrm{\#}\text{1}}^{2}a}{b-\sqrt{b^2-4a}}+1}F(i{\sinh }^{-1}\left(\sqrt{2}\sqrt{\frac{a}{b+\sqrt{b^2-4a}}}\mathrm{\#}\text{1}\right)|\frac{b+\sqrt{b^2-4a}}{b-\sqrt{b^2-4a}})}{\sqrt{2}\sqrt{\frac{a}{\sqrt{b^2-4a}+b}}\sqrt{{\mathrm{\#}\text{1}}^{4}a+{\mathrm{\#}\text{1}}^{2}b+1}}\mathrm{\&}][c_1-\frac{i\sqrt{\frac{\sqrt{b^2-4a}+2a{x}^2+b}{\sqrt{b^2-4a}+b}}\sqrt{\frac{2a{x}^2}{b-\sqrt{b^2-4a}}+1}F(i{\sinh }^{-1}\left(\sqrt{2}\sqrt{\frac{a}{b+\sqrt{b^2-4a}}}x\right)|\frac{b+\sqrt{b^2-4a}}{b-\sqrt{b^2-4a}})}{\sqrt{2}\sqrt{\frac{a}{\sqrt{b^2-4a}+b}}\sqrt{a{x}^4+b{x}^2+1}}]\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 77 $$\{{\int }^{y\left(x\right)}\frac{1}{\sqrt{{\mathit{\_}\mathit{a}}^{4}a+{\mathit{\_}\mathit{a}}^{2}b+1}}d\mathit{\_}\mathit{a}+{\int }^x-1\sqrt{\frac{a{\left(y\left(x\right)\right)}^4+b{\left(y\left(x\right)\right)}^2+1}{{\mathit{\_}\mathit{a}}^{4}a+{\mathit{\_}\mathit{a}}^{2}b+1}}\frac{1}{\sqrt{a{\left(y\left(x\right)\right)}^4+b{\left(y\left(x\right)\right)}^2+1}}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$

Sage: cpu = 0 (sec), leaf count = 0 $$\text{Maxima was unable to solve this ODE}$$