ODE
\[ x^2 y'(x)=a+b x^2 y(x)^2 \] ODE Classification
[[_homogeneous, `class G`], _rational, [_Riccati, _special]]
Book solution method
Riccati ODE, Main form
Mathematica ✓
cpu = 0.250604 (sec), leaf count = 51
\[\left \{\left \{y(x)\to \frac {-1+\sqrt {1-4 a b} \left (-1+\frac {2 c_1}{x^{\sqrt {1-4 a b}}+c_1}\right )}{2 b x}\right \}\right \}\]
Maple ✓
cpu = 0.044 (sec), leaf count = 48
\[\left [y \left (x \right ) = -\frac {\tan \left (-\frac {\ln \left (x \right ) \sqrt {4 a b -1}}{2}+\frac {\textit {\_C1} \sqrt {4 a b -1}}{2}\right ) \sqrt {4 a b -1}+1}{2 b x}\right ]\] Mathematica raw input
DSolve[x^2*y'[x] == a + b*x^2*y[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> (-1 + Sqrt[1 - 4*a*b]*(-1 + (2*C[1])/(x^Sqrt[1 - 4*a*b] + C[1])))/(2*b*x)}}
Maple raw input
dsolve(x^2*diff(y(x),x) = a+b*x^2*y(x)^2, y(x))
Maple raw output
[y(x) = -1/2*(tan(-1/2*ln(x)*(4*a*b-1)^(1/2)+1/2*_C1*(4*a*b-1)^(1/2))*(4*a*b-1)^(1/2)+1)/b/x]