ODE
\[ y'(x)=(9 y(x)+4 x+1)^2 \] ODE Classification
[[_homogeneous, `class C`], _Riccati]
Book solution method
Equation linear in the variables, \(y'(x)=f(a+b x+ c y(x))\)
Mathematica ✓
cpu = 0.0174784 (sec), leaf count = 34
\[\left \{\left \{y(x)\to \frac {1}{81} \left (\frac {1}{c_1 e^{12 i x}-\frac {i}{12}}-36 x-(9+6 i)\right )\right \}\right \}\]
Maple ✓
cpu = 0.04 (sec), leaf count = 20
\[ \left \{ -{\frac {1}{6}\arctan \left ( {\frac {27\,y \left ( x \right ) }{2}}+6\,x+{\frac {3}{2}} \right ) }+x-{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[y'[x] == (1 + 4*x + 9*y[x])^2,y[x],x]
Mathematica raw output
{{y[x] -> ((-9 - 6*I) - 36*x + (-I/12 + E^((12*I)*x)*C[1])^(-1))/81}}
Maple raw input
dsolve(diff(y(x),x) = (1+4*x+9*y(x))^2, y(x),'implicit')
Maple raw output
-1/6*arctan(27/2*y(x)+6*x+3/2)+x-_C1 = 0