ODE
\[ x^2 y'(x)=a+b x y(x)+c x^2 y(x)^2 \] ODE Classification
[[_homogeneous, `class G`], _rational, _Riccati]
Book solution method
Riccati ODE, Generalized ODE
Mathematica ✓
cpu = 0.0331989 (sec), leaf count = 64
\[\left \{\left \{y(x)\to -\frac {\sqrt {-4 a c+b^2+2 b+1} \left (1-\frac {2 c_1}{x^{\sqrt {-4 a c+b^2+2 b+1}}+c_1}\right )+b+1}{2 c x}\right \}\right \}\]
Maple ✓
cpu = 0.011 (sec), leaf count = 54
\[ \left \{ \ln \left ( x \right ) -{\it \_C1}-2\,{\frac {1}{\sqrt {4\,ca-{b}^{2}-2\,b-1}}\arctan \left ( {\frac {2\,cxy \left ( x \right ) +b+1}{\sqrt {4\,ca-{b}^{2}-2\,b-1}}} \right ) }=0 \right \} \] Mathematica raw input
DSolve[x^2*y'[x] == a + b*x*y[x] + c*x^2*y[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> -(1 + b + Sqrt[1 + 2*b + b^2 - 4*a*c]*(1 - (2*C[1])/(x^Sqrt[1 + 2*b + b^2 - 4*a*c] + C[1])))/(2*c*x)}}
Maple raw input
dsolve(x^2*diff(y(x),x) = a+b*x*y(x)+c*x^2*y(x)^2, y(x),'implicit')
Maple raw output
ln(x)-_C1-2/(4*a*c-b^2-2*b-1)^(1/2)*arctan((2*c*x*y(x)+b+1)/(4*a*c-b^2-2*b-1)^(1/2)) = 0