2.478   ODE No. 478

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

$$(y^{\prime }(x{)}^2+1)(ay(x)+b)-c=0$$ ✓ Mathematica : cpu = 0.167435 (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 = 0.085 (sec), leaf count = 88

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