4.1.45 \(y'(x)=(x-y(x))^2+3 (y(x)-x+1)\)

ODE
\[ y'(x)=(x-y(x))^2+3 (y(x)-x+1) \] 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 = 0.0180019 (sec), leaf count = 18

\[\left \{\left \{y(x)\to \frac {1}{c_1 e^x+1}+x-2\right \}\right \}\]

Maple
cpu = 0.028 (sec), leaf count = 26

\[ \left \{ \ln \left (-x+y \relax (x ) +2 \right ) -\ln \left (y \relax (x ) -x+1 \right ) +x-{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[y'[x] == (x - y[x])^2 + 3*(1 - x + y[x]),y[x],x]

Mathematica raw output

{{y[x] -> -2 + x + (1 + E^x*C[1])^(-1)}}

Maple raw input

dsolve(diff(y(x),x) = 3-3*x+3*y(x)+(x-y(x))^2, y(x),'implicit')

Maple raw output

ln(-x+y(x)+2)-ln(y(x)-x+1)+x-_C1 = 0