\[ (y(x)+3 x-1)^2 y'(x)-(2 y(x)-1) (4 y(x)+6 x-3)=0 \] ✓ Mathematica : cpu = 0.229853 (sec), leaf count = 2129
DSolve[-((-1 + 2*y[x])*(-3 + 6*x + 4*y[x])) + (-1 + 3*x + y[x])^2*Derivative[1][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {1}{6} \left (12 x+4 e^{c_1}+1\right )-\frac {1}{6} \sqrt {36 x^2+96 e^{c_1} x-12 x-16 e^{c_1}+16 e^{2 c_1}+3\ 2^{2/3} \sqrt [3]{-7776 e^{c_1} x^5+6480 e^{c_1} x^4-1296 e^{2 c_1} x^4-2160 e^{c_1} x^3+864 e^{2 c_1} x^3+360 e^{c_1} x^2-216 e^{2 c_1} x^2-30 e^{c_1} x+24 e^{2 c_1} x+e^{c_1}-e^{2 c_1}}+1}-\frac {1}{2} \sqrt {\frac {2}{9} \left (12 x+4 e^{c_1}+1\right ){}^2-\frac {8}{3} \left (9 x^2+3 x+2 e^{c_1}\right )-\frac {1}{3} 2^{2/3} \sqrt [3]{-7776 e^{c_1} x^5+6480 e^{c_1} x^4-1296 e^{2 c_1} x^4-2160 e^{c_1} x^3+864 e^{2 c_1} x^3+360 e^{c_1} x^2-216 e^{2 c_1} x^2-30 e^{c_1} x+24 e^{2 c_1} x+e^{c_1}-e^{2 c_1}}-\frac {3 \left (\frac {8}{27} \left (12 x+4 e^{c_1}+1\right ){}^3-\frac {16}{3} \left (9 x^2+3 x+2 e^{c_1}\right ) \left (12 x+4 e^{c_1}+1\right )+16 \left (9 x^2+e^{c_1}\right )\right )}{4 \sqrt {36 x^2+96 e^{c_1} x-12 x-16 e^{c_1}+16 e^{2 c_1}+3\ 2^{2/3} \sqrt [3]{-7776 e^{c_1} x^5+6480 e^{c_1} x^4-1296 e^{2 c_1} x^4-2160 e^{c_1} x^3+864 e^{2 c_1} x^3+360 e^{c_1} x^2-216 e^{2 c_1} x^2-30 e^{c_1} x+24 e^{2 c_1} x+e^{c_1}-e^{2 c_1}}+1}}}\right \},\left \{y(x)\to \frac {1}{6} \left (12 x+4 e^{c_1}+1\right )-\frac {1}{6} \sqrt {36 x^2+96 e^{c_1} x-12 x-16 e^{c_1}+16 e^{2 c_1}+3\ 2^{2/3} \sqrt [3]{-7776 e^{c_1} x^5+6480 e^{c_1} x^4-1296 e^{2 c_1} x^4-2160 e^{c_1} x^3+864 e^{2 c_1} x^3+360 e^{c_1} x^2-216 e^{2 c_1} x^2-30 e^{c_1} x+24 e^{2 c_1} x+e^{c_1}-e^{2 c_1}}+1}+\frac {1}{2} \sqrt {\frac {2}{9} \left (12 x+4 e^{c_1}+1\right ){}^2-\frac {8}{3} \left (9 x^2+3 x+2 e^{c_1}\right )-\frac {1}{3} 2^{2/3} \sqrt [3]{-7776 e^{c_1} x^5+6480 e^{c_1} x^4-1296 e^{2 c_1} x^4-2160 e^{c_1} x^3+864 e^{2 c_1} x^3+360 e^{c_1} x^2-216 e^{2 c_1} x^2-30 e^{c_1} x+24 e^{2 c_1} x+e^{c_1}-e^{2 c_1}}-\frac {3 \left (\frac {8}{27} \left (12 x+4 e^{c_1}+1\right ){}^3-\frac {16}{3} \left (9 x^2+3 x+2 e^{c_1}\right ) \left (12 x+4 e^{c_1}+1\right )+16 \left (9 x^2+e^{c_1}\right )\right )}{4 \sqrt {36 x^2+96 e^{c_1} x-12 x-16 e^{c_1}+16 e^{2 c_1}+3\ 2^{2/3} \sqrt [3]{-7776 e^{c_1} x^5+6480 e^{c_1} x^4-1296 e^{2 c_1} x^4-2160 e^{c_1} x^3+864 e^{2 c_1} x^3+360 e^{c_1} x^2-216 e^{2 c_1} x^2-30 e^{c_1} x+24 e^{2 c_1} x+e^{c_1}-e^{2 c_1}}+1}}}\right \},\left \{y(x)\to \frac {1}{6} \left (12 x+4 e^{c_1}+1\right )+\frac {1}{6} \sqrt {36 x^2+96 e^{c_1} x-12 x-16 e^{c_1}+16 e^{2 c_1}+3\ 2^{2/3} \sqrt [3]{-7776 e^{c_1} x^5+6480 e^{c_1} x^4-1296 e^{2 c_1} x^4-2160 e^{c_1} x^3+864 e^{2 c_1} x^3+360 e^{c_1} x^2-216 e^{2 c_1} x^2-30 e^{c_1} x+24 e^{2 c_1} x+e^{c_1}-e^{2 c_1}}+1}-\frac {1}{2} \sqrt {\frac {2}{9} \left (12 x+4 e^{c_1}+1\right ){}^2-\frac {8}{3} \left (9 x^2+3 x+2 e^{c_1}\right )-\frac {1}{3} 2^{2/3} \sqrt [3]{-7776 e^{c_1} x^5+6480 e^{c_1} x^4-1296 e^{2 c_1} x^4-2160 e^{c_1} x^3+864 e^{2 c_1} x^3+360 e^{c_1} x^2-216 e^{2 c_1} x^2-30 e^{c_1} x+24 e^{2 c_1} x+e^{c_1}-e^{2 c_1}}+\frac {3 \left (\frac {8}{27} \left (12 x+4 e^{c_1}+1\right ){}^3-\frac {16}{3} \left (9 x^2+3 x+2 e^{c_1}\right ) \left (12 x+4 e^{c_1}+1\right )+16 \left (9 x^2+e^{c_1}\right )\right )}{4 \sqrt {36 x^2+96 e^{c_1} x-12 x-16 e^{c_1}+16 e^{2 c_1}+3\ 2^{2/3} \sqrt [3]{-7776 e^{c_1} x^5+6480 e^{c_1} x^4-1296 e^{2 c_1} x^4-2160 e^{c_1} x^3+864 e^{2 c_1} x^3+360 e^{c_1} x^2-216 e^{2 c_1} x^2-30 e^{c_1} x+24 e^{2 c_1} x+e^{c_1}-e^{2 c_1}}+1}}}\right \},\left \{y(x)\to \frac {1}{6} \left (12 x+4 e^{c_1}+1\right )+\frac {1}{6} \sqrt {36 x^2+96 e^{c_1} x-12 x-16 e^{c_1}+16 e^{2 c_1}+3\ 2^{2/3} \sqrt [3]{-7776 e^{c_1} x^5+6480 e^{c_1} x^4-1296 e^{2 c_1} x^4-2160 e^{c_1} x^3+864 e^{2 c_1} x^3+360 e^{c_1} x^2-216 e^{2 c_1} x^2-30 e^{c_1} x+24 e^{2 c_1} x+e^{c_1}-e^{2 c_1}}+1}+\frac {1}{2} \sqrt {\frac {2}{9} \left (12 x+4 e^{c_1}+1\right ){}^2-\frac {8}{3} \left (9 x^2+3 x+2 e^{c_1}\right )-\frac {1}{3} 2^{2/3} \sqrt [3]{-7776 e^{c_1} x^5+6480 e^{c_1} x^4-1296 e^{2 c_1} x^4-2160 e^{c_1} x^3+864 e^{2 c_1} x^3+360 e^{c_1} x^2-216 e^{2 c_1} x^2-30 e^{c_1} x+24 e^{2 c_1} x+e^{c_1}-e^{2 c_1}}+\frac {3 \left (\frac {8}{27} \left (12 x+4 e^{c_1}+1\right ){}^3-\frac {16}{3} \left (9 x^2+3 x+2 e^{c_1}\right ) \left (12 x+4 e^{c_1}+1\right )+16 \left (9 x^2+e^{c_1}\right )\right )}{4 \sqrt {36 x^2+96 e^{c_1} x-12 x-16 e^{c_1}+16 e^{2 c_1}+3\ 2^{2/3} \sqrt [3]{-7776 e^{c_1} x^5+6480 e^{c_1} x^4-1296 e^{2 c_1} x^4-2160 e^{c_1} x^3+864 e^{2 c_1} x^3+360 e^{c_1} x^2-216 e^{2 c_1} x^2-30 e^{c_1} x+24 e^{2 c_1} x+e^{c_1}-e^{2 c_1}}+1}}}\right \}\right \}\] ✓ Maple : cpu = 0.328 (sec), leaf count = 71
dsolve((y(x)+3*x-1)^2*diff(y(x),x)-(2*y(x)-1)*(4*y(x)+6*x-3) = 0,y(x))
\[-\ln \left (\frac {-6 y \left (x \right )+4-6 x}{6 x -1}\right )+3 \ln \left (\frac {-6 y \left (x \right )+3}{6 x -1}\right )-3 \ln \left (\frac {-6 y \left (x \right )+18 x}{6 x -1}\right )-\ln \left (6 x -1\right )-c_{1} = 0\]