4.2.3 \(y'(x)=(9 y(x)+4 x+1)^2\)

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

\[ \left \{ -{\frac {1}{6}\arctan \left ({\frac {27\,y \relax (x ) }{2}}+6\,x+{\frac {3}{2}} \right ) }+x-{\it \_C1}=0 \right \} \] 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