4.2.2 \(y'(x)=(-4 y(x)+x+3)^2\)

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

\[ \left \{ -\ln \left (-2\,x+8\,y \relax (x ) -7 \right ) +\ln \left (-2\,x+8\,y \relax (x ) -5 \right ) +4\,x-{\it \_C1}=0 \right \} \] 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