ODE No. 1781

\[ \left (y(x)^2+1\right ) y''(x)+(1-2 y(x)) y'(x)^2=0 \]

✓ Mathematica : cpu = 0.230052 (sec), leaf count = 46

DSolve[(1 - 2*y[x])*Derivative[1][y][x]^2 + (1 + y[x]^2)*Derivative[2][y][x] == 0,y[x],x]

\[\left \{\left \{y(x)\to \frac {i \left (1-c_1{}^{2 i} (x+c_2){}^{2 i}\right )}{1+c_1{}^{2 i} (x+c_2){}^{2 i}}\right \}\right \}\]

✓ Maple : cpu = 0.056 (sec), leaf count = 11

dsolve((y(x)^2+1)*diff(diff(y(x),x),x)+(1-2*y(x))*diff(y(x),x)^2=0,y(x))

\[y \left (x \right ) = \tan \left (\ln \left (x c_{1} +c_{2} \right )\right )\]