ODE
\[ \left (y(x)^2+1\right ) y''(x)+(1-2 y(x)) y'(x)^2=0 \] ODE Classification
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.08824 (sec), leaf count = 14
\[\left \{\left \{y(x)\to \tan \left (\log \left (c_1 \left (c_2+x\right )\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.025 (sec), leaf count = 15
\[ \left \{ {{\rm e}^{\arctan \left ( y \left ( x \right ) \right ) }}-{\it \_C1}\,x-{\it \_C2}=0 \right \} \] Mathematica raw input
DSolve[(1 - 2*y[x])*y'[x]^2 + (1 + y[x]^2)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> Tan[Log[C[1]*(x + C[2])]]}}
Maple raw input
dsolve((1+y(x)^2)*diff(diff(y(x),x),x)+(1-2*y(x))*diff(y(x),x)^2 = 0, y(x),'implicit')
Maple raw output
exp(arctan(y(x)))-_C1*x-_C2 = 0