ODE
\[ y'(x)=(-4 y(x)+x+3)^2 \] 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 = 0.240557 (sec), leaf count = 28
\[\left \{\left \{y(x)\to \frac {1}{16} \left (4 x+\frac {1}{\frac {1}{4}+c_1 e^{4 x}}+10\right )\right \}\right \}\]
Maple ✓
cpu = 0.138 (sec), leaf count = 36
\[\left [y \left (x \right ) = \frac {2 x \,{\mathrm e}^{4 x} \textit {\_C1} +5 \,{\mathrm e}^{4 x} \textit {\_C1} -2 x -7}{-8+8 \,{\mathrm e}^{4 x} \textit {\_C1}}\right ]\] Mathematica raw input
DSolve[y'[x] == (3 + x - 4*y[x])^2,y[x],x]
Mathematica raw output
{{y[x] -> (10 + 4*x + (1/4 + E^(4*x)*C[1])^(-1))/16}}
Maple raw input
dsolve(diff(y(x),x) = (3+x-4*y(x))^2, y(x))
Maple raw output
[y(x) = 1/8*(2*x*exp(x)^4*_C1+5*exp(x)^4*_C1-2*x-7)/(-1+exp(x)^4*_C1)]