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 = 0.0161134 (sec), leaf count = 28
\[\left \{\left \{y(x)\to \frac {1}{16} \left (\frac {1}{c_1 e^{4 x}+\frac {1}{4}}+4 x+10\right )\right \}\right \}\]
Maple ✓
cpu = 0.033 (sec), leaf count = 32
\[ \left \{ -\ln \left ( -2\,x+8\,y \left ( x \right ) -7 \right ) +\ln \left ( -2\,x+8\,y \left ( x \right ) -5 \right ) +4\,x-{\it \_C1}=0 \right \} \] 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),'implicit')
Maple raw output
-ln(-2*x+8*y(x)-7)+ln(-2*x+8*y(x)-5)+4*x-_C1 = 0