ODE
\[ 4 (-y(x)-x+1) y'(x)-x+2=0 \] ODE Classification
[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class C`], _dAlembert]
Book solution method
Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)
Mathematica ✓
cpu = 6.12883 (sec), leaf count = 109
\[\text {Solve}\left [\frac {2^{2/3} \left (x \log \left (\frac {x-2}{y(x)+x-1}\right )-x \log \left (\frac {2 y(x)+x}{y(x)+x-1}\right )+2 y(x) \left (\log \left (\frac {x-2}{y(x)+x-1}\right )-\log \left (\frac {2 y(x)+x}{y(x)+x-1}\right )+1\right )+2 x-2\right )}{9 (2 y(x)+x)}=\frac {1}{9} 2^{2/3} \log (x-2)+c_1,y(x)\right ]\]
Maple ✓
cpu = 0.128 (sec), leaf count = 29
\[\left [y \left (x \right ) = -1-\frac {\left (x -2\right ) \left (-1+\LambertW \left (-\textit {\_C1} \left (x -2\right )\right )\right )}{2 \LambertW \left (-\textit {\_C1} \left (x -2\right )\right )}\right ]\] Mathematica raw input
DSolve[2 - x + 4*(1 - x - y[x])*y'[x] == 0,y[x],x]
Mathematica raw output
Solve[(2^(2/3)*(-2 + 2*x + x*Log[(-2 + x)/(-1 + x + y[x])] - x*Log[(x + 2*y[x])/(-1 + x + y[x])] + 2*(1 + Log[(-2 + x)/(-1 + x + y[x])] - Log[(x + 2*y[x])/(-1 + x + y[x])])*y[x]))/(9*(x + 2*y[x])) == C[1] + (2^(2/3)*Log[-2 + x])/9, y[x]]
Maple raw input
dsolve(4*(1-x-y(x))*diff(y(x),x)+2-x = 0, y(x))
Maple raw output
[y(x) = -1-1/2*(x-2)*(-1+LambertW(-_C1*(x-2)))/LambertW(-_C1*(x-2))]