2.1782   ODE No. 1782

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

$$(y(x{)}^2+1)y^{″}(x)-3y(x)y^{\prime }(x{)}^2=0$$ ✓ Mathematica : cpu = 0.157387 (sec), leaf count = 93

$$\{\{y(x)\to -\frac{i{c}_1(x+c_2)}{\sqrt{c_1{}^2{x}^2+2c_2{c}_1{}^{2}x-1+c_2{}^2{c}_1{}^2}}\},\{y(x)\to \frac{i{c}_1(x+c_2)}{\sqrt{c_1{}^2{x}^2+2c_2{c}_1{}^{2}x-1+c_2{}^2{c}_1{}^2}}\}\}$$ ✓ Maple : cpu = 0.24 (sec), leaf count = 33

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