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 = 0.242229 (sec), leaf count = 24
\[\left \{\left \{y(x)\to \frac {i \tan \left (\frac {1}{2} i \log (x)+c_1\right )}{x}\right \}\right \}\]
Maple ✓
cpu = 0.035 (sec), leaf count = 17
\[\left [y \left (x \right ) = \frac {\tanh \left (-\frac {\ln \left (x \right )}{2}+\frac {\textit {\_C1}}{2}\right )}{x}\right ]\] 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))
Maple raw output
[y(x) = tanh(-1/2*ln(x)+1/2*_C1)/x]