ODE
\[ (-y(x)-3 x+1)^2 y'(x)=(-4 y(x)-6 x+3) (1-2 y(x)) \] ODE Classification
[[_homogeneous, `class C`], _rational]
Book solution method
Change of Variable, Two new variables
Mathematica ✓
cpu = 0.503344 (sec), leaf count = 1089
\[\left \{\left \{y(x)\to \frac {1}{6} \left (12 x+4 e^{c_1}-\sqrt {36 x^2-12 x+16 e^{2 c_1}+16 e^{c_1} (6 x-1)+3\ 2^{2/3} \sqrt [3]{-e^{c_1} (6 x-1)^4 \left (6 x+e^{c_1}-1\right )}+1}-\frac {1}{2} \sqrt {8 \left (12 x+4 e^{c_1}+1\right ){}^2-96 \left (3 x (3 x+1)+2 e^{c_1}\right )-12\ 2^{2/3} \sqrt [3]{-e^{c_1} (6 x-1)^4 \left (6 x+e^{c_1}-1\right )}-\frac {8 \left (-(6 x-1)^3+96 e^{2 c_1} (6 x-1)+64 e^{3 c_1}+30 e^{c_1} (1-6 x)^2\right )}{\sqrt {36 x^2-12 x+16 e^{2 c_1}+16 e^{c_1} (6 x-1)+3\ 2^{2/3} \sqrt [3]{-e^{c_1} (6 x-1)^4 \left (6 x+e^{c_1}-1\right )}+1}}}+1\right )\right \},\left \{y(x)\to \frac {1}{6} \left (12 x+4 e^{c_1}-\sqrt {36 x^2-12 x+16 e^{2 c_1}+16 e^{c_1} (6 x-1)+3\ 2^{2/3} \sqrt [3]{-e^{c_1} (6 x-1)^4 \left (6 x+e^{c_1}-1\right )}+1}+\frac {1}{2} \sqrt {8 \left (12 x+4 e^{c_1}+1\right ){}^2-96 \left (3 x (3 x+1)+2 e^{c_1}\right )-12\ 2^{2/3} \sqrt [3]{-e^{c_1} (6 x-1)^4 \left (6 x+e^{c_1}-1\right )}-\frac {8 \left (-(6 x-1)^3+96 e^{2 c_1} (6 x-1)+64 e^{3 c_1}+30 e^{c_1} (1-6 x)^2\right )}{\sqrt {36 x^2-12 x+16 e^{2 c_1}+16 e^{c_1} (6 x-1)+3\ 2^{2/3} \sqrt [3]{-e^{c_1} (6 x-1)^4 \left (6 x+e^{c_1}-1\right )}+1}}}+1\right )\right \},\left \{y(x)\to \frac {1}{6} \left (12 x+4 e^{c_1}+\sqrt {36 x^2-12 x+16 e^{2 c_1}+16 e^{c_1} (6 x-1)+3\ 2^{2/3} \sqrt [3]{-e^{c_1} (6 x-1)^4 \left (6 x+e^{c_1}-1\right )}+1}-\frac {1}{2} \sqrt {8 \left (12 x+4 e^{c_1}+1\right ){}^2-96 \left (3 x (3 x+1)+2 e^{c_1}\right )-12\ 2^{2/3} \sqrt [3]{-e^{c_1} (6 x-1)^4 \left (6 x+e^{c_1}-1\right )}+\frac {8 \left (-(6 x-1)^3+96 e^{2 c_1} (6 x-1)+64 e^{3 c_1}+30 e^{c_1} (1-6 x)^2\right )}{\sqrt {36 x^2-12 x+16 e^{2 c_1}+16 e^{c_1} (6 x-1)+3\ 2^{2/3} \sqrt [3]{-e^{c_1} (6 x-1)^4 \left (6 x+e^{c_1}-1\right )}+1}}}+1\right )\right \},\left \{y(x)\to \frac {1}{6} \left (12 x+4 e^{c_1}+\sqrt {36 x^2-12 x+16 e^{2 c_1}+16 e^{c_1} (6 x-1)+3\ 2^{2/3} \sqrt [3]{-e^{c_1} (6 x-1)^4 \left (6 x+e^{c_1}-1\right )}+1}+\frac {1}{2} \sqrt {8 \left (12 x+4 e^{c_1}+1\right ){}^2-96 \left (3 x (3 x+1)+2 e^{c_1}\right )-12\ 2^{2/3} \sqrt [3]{-e^{c_1} (6 x-1)^4 \left (6 x+e^{c_1}-1\right )}+\frac {8 \left (-(6 x-1)^3+96 e^{2 c_1} (6 x-1)+64 e^{3 c_1}+30 e^{c_1} (1-6 x)^2\right )}{\sqrt {36 x^2-12 x+16 e^{2 c_1}+16 e^{c_1} (6 x-1)+3\ 2^{2/3} \sqrt [3]{-e^{c_1} (6 x-1)^4 \left (6 x+e^{c_1}-1\right )}+1}}}+1\right )\right \}\right \}\]
Maple ✓
cpu = 0.336 (sec), leaf count = 72
\[\left [3 \ln \left (\frac {-6 y \left (x \right )+3}{6 x -1}\right )-3 \ln \left (\frac {-6 y \left (x \right )+18 x}{6 x -1}\right )-\ln \left (-\frac {6 y \left (x \right )-4+6 x}{6 x -1}\right )-\ln \left (6 x -1\right )-\textit {\_C1} = 0\right ]\] Mathematica raw input
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 - 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}}
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))
Maple raw output
[3*ln((-6*y(x)+3)/(6*x-1))-3*ln((-6*y(x)+18*x)/(6*x-1))-ln(-(6*y(x)-4+6*x)/(6*x-1))-ln(6*x-1)-_C1 = 0]