2.1653   ODE No. 1653

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

$$y^{″}(x)-a{(y^{\prime }(x{)}^2+1)}^{3/2}=0$$ ✓ Mathematica : cpu = 0.0663388 (sec), leaf count = 75

$$\{\{y(x)\to c_2-\frac{i\sqrt{a^2{x}^2+2a{c}_{1}x+c_1^2-1}}{a}\},\{y(x)\to c_2+\frac{i\sqrt{a^2{x}^2+2a{c}_{1}x+c_1^2-1}}{a}\}\}$$

✓ Maple : cpu = 0.135 (sec), leaf count = 55

$$\{y\left(x\right)=\frac{(\mathit{\_}\mathit{C}\mathit{1}a+ax+1)(\mathit{\_}\mathit{C}\mathit{1}a+ax-1)}{a}\sqrt{-{({\mathit{\_}\mathit{C}\mathit{1}}^2{a}^2+2\mathit{\_}\mathit{C}\mathit{1}{a}^{2}x+a^2{x}^2-1)}^{-1}}+\mathit{\_}\mathit{C}\mathit{2}\}$$