2.1700   ODE No. 1700

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

$$y(x)y^{″}(x)-y^{\prime }(x{)}^2+1=0$$ ✓ Mathematica : cpu = 0.0837369 (sec), leaf count = 44

$$\{\{y(x)\to -e^{-c_1}\sinh \left(e^{c_1}(c_2+x)\right)\},\{y(x)\to e^{-c_1}\sinh \left(e^{c_1}(c_2+x)\right)\}\}$$

✓ Maple : cpu = 0.392 (sec), leaf count = 86

$$\{y\left(x\right)=\frac{1}{2}(-\mathit{\_}\mathit{C}\mathit{1}{\left({\mathrm{e}}^{\frac{x}{\mathit{\_}\mathit{C}\mathit{1}}}\right)}^2{\left({\mathrm{e}}^{\frac{\mathit{\_}\mathit{C}\mathit{2}}{\mathit{\_}\mathit{C}\mathit{1}}}\right)}^2+\mathit{\_}\mathit{C}\mathit{1}){\left({\mathrm{e}}^{\frac{\mathit{\_}\mathit{C}\mathit{2}}{\mathit{\_}\mathit{C}\mathit{1}}}\right)}^{-1}{\left({\mathrm{e}}^{\frac{x}{\mathit{\_}\mathit{C}\mathit{1}}}\right)}^{-1},y\left(x\right)=\frac{1}{2}(\mathit{\_}\mathit{C}\mathit{1}{\left({\mathrm{e}}^{\frac{x}{\mathit{\_}\mathit{C}\mathit{1}}}\right)}^2{\left({\mathrm{e}}^{\frac{\mathit{\_}\mathit{C}\mathit{2}}{\mathit{\_}\mathit{C}\mathit{1}}}\right)}^2-\mathit{\_}\mathit{C}\mathit{1}){\left({\mathrm{e}}^{\frac{\mathit{\_}\mathit{C}\mathit{2}}{\mathit{\_}\mathit{C}\mathit{1}}}\right)}^{-1}{\left({\mathrm{e}}^{\frac{x}{\mathit{\_}\mathit{C}\mathit{1}}}\right)}^{-1}\}$$