2.1785   ODE No. 1785

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

$$(x^2+y(x{)}^2)y^{″}(x)-2(x{y}^{\prime }(x)-y(x))(y^{\prime }(x{)}^2+1)=0$$ ✓ Mathematica : cpu = 0.443759 (sec), leaf count = 95

$$\{\{y(x)\to \frac{1}{2}(-\sqrt{4x(-x+e^{c_2})+e^{2c_2}{\cot }^2(c_1)}-e^{c_2}\cot (c_1))\},\{y(x)\to \frac{1}{2}(\sqrt{4x(-x+e^{c_2})+e^{2c_2}{\cot }^2(c_1)}-e^{c_2}\cot (c_1))\}\}$$ ✓ Maple : cpu = 1.649 (sec), leaf count = 83

$$\{y\left(x\right)=\frac{c_1+1-\sqrt{-4c_2^2{x}^2+c_1^2-4i{c}_{2}x+c_1(4i{c}_{2}x+2)+1}}{2c_2},y\left(x\right)=\frac{c_1+1+\sqrt{-4c_2^2{x}^2+c_1^2-4i{c}_{2}x+c_1(4i{c}_{2}x+2)+1}}{2c_2}\}$$