3.478   ODE No. 478

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

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

Mathematica: cpu = 0.166521 (sec), leaf count = 141 $$\{\{y(x)\to \text{InverseFunction}\left[\frac{c{\tan }^{-1}\left(\frac{\sqrt{\mathrm{\#}\text{1}a+b}}{\sqrt{-\mathrm{\#}\text{1}a-b+c}}\right)-\sqrt{\mathrm{\#}\text{1}a+b}\sqrt{-\mathrm{\#}\text{1}a-b+c}}{a}\mathrm{\&}\right][c_1-x]\},\{y(x)\to \text{InverseFunction}\left[\frac{c{\tan }^{-1}\left(\frac{\sqrt{\mathrm{\#}\text{1}a+b}}{\sqrt{-\mathrm{\#}\text{1}a-b+c}}\right)-\sqrt{\mathrm{\#}\text{1}a+b}\sqrt{-\mathrm{\#}\text{1}a-b+c}}{a}\mathrm{\&}\right][c_1+x]\}\}$$

Maple: cpu = 0.609 (sec), leaf count = 88 $$\{x-{\int }^{y\left(x\right)}(\mathit{\_}\mathit{a}a+b)\frac{1}{\sqrt{-(\mathit{\_}\mathit{a}a+b)(\mathit{\_}\mathit{a}a+b-c)}}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0,x-{\int }^{y\left(x\right)}-(\mathit{\_}\mathit{a}a+b)\frac{1}{\sqrt{-(\mathit{\_}\mathit{a}a+b)(\mathit{\_}\mathit{a}a+b-c)}}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0,y\left(x\right)=\frac{-b+c}{a}\}$$