[[_homogeneous, `class C`], _rational]
Book solution method
Change of Variable, Two new variables
Mathematica ✓
cpu = 0.217348 (sec), leaf count = 1089
Maple ✓
cpu = 0.039 (sec), leaf count = 71
DSolve[(1 - 3*x - y[x])^2*y'[x] == (3 - 6*x - 4*y[x])*(1 - 2*y[x]),y[x],x]
Mathematica raw output
{{y[x] -> (1 + 4*E^C[1] + 12*x - Sqrt[1 + 16*E^(2*C[1]) - 12*x + 36*x^2 + 16*E^C
[1]*(-1 + 6*x) + 3*2^(2/3)*(-(E^C[1]*(-1 + 6*x)^4*(-1 + E^C[1] + 6*x)))^(1/3)] -
Sqrt[-12*2^(2/3)*(-(E^C[1]*(-1 + 6*x)^4*(-1 + E^C[1] + 6*x)))^(1/3) + 8*(1 + 4*
E^C[1] + 12*x)^2 - 96*(2*E^C[1] + 3*x*(1 + 3*x)) - (8*(64*E^(3*C[1]) + 30*E^C[1]
*(1 - 6*x)^2 + 96*E^(2*C[1])*(-1 + 6*x) - (-1 + 6*x)^3))/Sqrt[1 + 16*E^(2*C[1])
- 12*x + 36*x^2 + 16*E^C[1]*(-1 + 6*x) + 3*2^(2/3)*(-(E^C[1]*(-1 + 6*x)^4*(-1 +
E^C[1] + 6*x)))^(1/3)]]/2)/6}, {y[x] -> (1 + 4*E^C[1] + 12*x - Sqrt[1 + 16*E^(2*
C[1]) - 12*x + 36*x^2 + 16*E^C[1]*(-1 + 6*x) + 3*2^(2/3)*(-(E^C[1]*(-1 + 6*x)^4*
(-1 + E^C[1] + 6*x)))^(1/3)] + Sqrt[-12*2^(2/3)*(-(E^C[1]*(-1 + 6*x)^4*(-1 + E^C
[1] + 6*x)))^(1/3) + 8*(1 + 4*E^C[1] + 12*x)^2 - 96*(2*E^C[1] + 3*x*(1 + 3*x)) -
(8*(64*E^(3*C[1]) + 30*E^C[1]*(1 - 6*x)^2 + 96*E^(2*C[1])*(-1 + 6*x) - (-1 + 6*
x)^3))/Sqrt[1 + 16*E^(2*C[1]) - 12*x + 36*x^2 + 16*E^C[1]*(-1 + 6*x) + 3*2^(2/3)
*(-(E^C[1]*(-1 + 6*x)^4*(-1 + E^C[1] + 6*x)))^(1/3)]]/2)/6}, {y[x] -> (1 + 4*E^C
[1] + 12*x + Sqrt[1 + 16*E^(2*C[1]) - 12*x + 36*x^2 + 16*E^C[1]*(-1 + 6*x) + 3*2
^(2/3)*(-(E^C[1]*(-1 + 6*x)^4*(-1 + E^C[1] + 6*x)))^(1/3)] - Sqrt[-12*2^(2/3)*(-
(E^C[1]*(-1 + 6*x)^4*(-1 + E^C[1] + 6*x)))^(1/3) + 8*(1 + 4*E^C[1] + 12*x)^2 - 9
6*(2*E^C[1] + 3*x*(1 + 3*x)) + (8*(64*E^(3*C[1]) + 30*E^C[1]*(1 - 6*x)^2 + 96*E^
(2*C[1])*(-1 + 6*x) - (-1 + 6*x)^3))/Sqrt[1 + 16*E^(2*C[1]) - 12*x + 36*x^2 + 16
*E^C[1]*(-1 + 6*x) + 3*2^(2/3)*(-(E^C[1]*(-1 + 6*x)^4*(-1 + E^C[1] + 6*x)))^(1/3
)]]/2)/6}, {y[x] -> (1 + 4*E^C[1] + 12*x + Sqrt[1 + 16*E^(2*C[1]) - 12*x + 36*x^
2 + 16*E^C[1]*(-1 + 6*x) + 3*2^(2/3)*(-(E^C[1]*(-1 + 6*x)^4*(-1 + E^C[1] + 6*x))
)^(1/3)] + Sqrt[-12*2^(2/3)*(-(E^C[1]*(-1 + 6*x)^4*(-1 + E^C[1] + 6*x)))^(1/3) +
8*(1 + 4*E^C[1] + 12*x)^2 - 96*(2*E^C[1] + 3*x*(1 + 3*x)) + (8*(64*E^(3*C[1]) +
30*E^C[1]*(1 - 6*x)^2 + 96*E^(2*C[1])*(-1 + 6*x) - (-1 + 6*x)^3))/Sqrt[1 + 16*E
^(2*C[1]) - 12*x + 36*x^2 + 16*E^C[1]*(-1 + 6*x) + 3*2^(2/3)*(-(E^C[1]*(-1 + 6*x
)^4*(-1 + E^C[1] + 6*x)))^(1/3)]]/2)/6}}
Maple raw input
dsolve((1-3*x-y(x))^2*diff(y(x),x) = (1-2*y(x))*(3-6*x-4*y(x)), y(x),'implicit')
Maple raw output
-ln((4-6*y(x)-6*x)/(6*x-1))-3*ln((18*x-6*y(x))/(6*x-1))+3*ln((3-6*y(x))/(6*x-1))
-ln(6*x-1)-_C1 = 0