\[ y'(x)^4+3 (x-1) y'(x)^2-3 (2 y(x)-1) y'(x)+3 x=0 \] ✓ Mathematica : cpu = 0.039006 (sec), leaf count = 113
DSolve[3*x - 3*(-1 + 2*y[x])*Derivative[1][y][x] + 3*(-1 + x)*Derivative[1][y][x]^2 + Derivative[1][y][x]^4 == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {1}{12} \left (-\sqrt {64 x^3+48 c_1{}^2 x^2+12 c_1{}^4 x+c_1{}^6}-6 c_1 x+6-c_1{}^3+6 c_1\right )\right \},\left \{y(x)\to \frac {1}{12} \left (\sqrt {64 x^3+48 c_1{}^2 x^2+12 c_1{}^4 x+c_1{}^6}-6 c_1 x+6-c_1{}^3+6 c_1\right )\right \}\right \}\] ✓ Maple : cpu = 0.104 (sec), leaf count = 171
dsolve(diff(y(x),x)^4+3*(x-1)*diff(y(x),x)^2-3*(2*y(x)-1)*diff(y(x),x)+3*x=0,y(x))
\[y \left (x \right ) = -x +\frac {5}{6}\]