ODE
\[ 2 x^2 y'(x)+x^2 \left (-y(x)^2\right )+2 x y(x)+1=0 \] ODE Classification
[[_homogeneous, `class G`], _rational, _Riccati]
Book solution method
Homogeneous equation, isobaric equation
Mathematica ✓
cpu = 0.00824596 (sec), leaf count = 24
\[\left \{\left \{y(x)\to \frac {i \tan \left (c_1+\frac {1}{2} i \log (x)\right )}{x}\right \}\right \}\]
Maple ✓
cpu = 0.009 (sec), leaf count = 16
\[ \left \{ \ln \left ( x \right ) -{\it \_C1}+2\,{\it Artanh} \left ( xy \left ( x \right ) \right ) =0 \right \} \] Mathematica raw input
DSolve[1 + 2*x*y[x] - x^2*y[x]^2 + 2*x^2*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (I*Tan[C[1] + (I/2)*Log[x]])/x}}
Maple raw input
dsolve(2*x^2*diff(y(x),x)+1+2*x*y(x)-x^2*y(x)^2 = 0, y(x),'implicit')
Maple raw output
ln(x)-_C1+2*arctanh(x*y(x)) = 0