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 = 0.254996 (sec), leaf count = 34
\[\left \{\left \{y(x)\to \frac {1}{81} \left (-36 x+\frac {1}{c_1 e^{12 i x}-\frac {i}{12}}-(9+6 i)\right )\right \}\right \}\]
Maple ✓
cpu = 0.044 (sec), leaf count = 19
\[\left [y \left (x \right ) = -\frac {4 x}{9}-\frac {1}{9}-\frac {2 \tan \left (-6 x +6 \textit {\_C1} \right )}{27}\right ]\] 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 + (-1/12*I + 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))
Maple raw output
[y(x) = -4/9*x-1/9-2/27*tan(-6*x+6*_C1)]