4.7.32 \(2 x^2 y'(x)+x^2 \left (-y(x)^2\right )+2 x y(x)+1=0\)

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

\[ \left \{ \ln \relax (x ) -{\it \_C1}+2\,{\it Artanh} \left (xy \relax (x ) \right ) =0 \right \} \] 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