\[ (3 x+1) y'(x)^2-3 (y(x)+2) y'(x)+9=0 \] ✓ Mathematica : cpu = 0.47024 (sec), leaf count = 310
\[\left \{\left \{y(x)\to -\frac {\sqrt {9 x^2 \sinh \left (c_1\right )+9 x^2 \cosh \left (c_1\right )-210 x \sinh \left (c_1\right )+6 x \sinh \left (2 c_1\right )-210 x \cosh \left (c_1\right )+6 x \cosh \left (2 c_1\right )+1225 \sinh \left (c_1\right )-70 \sinh \left (2 c_1\right )+\sinh \left (3 c_1\right )+1225 \cosh \left (c_1\right )-70 \cosh \left (2 c_1\right )+\cosh \left (3 c_1\right )}}{\sinh \left (c_1\right )+\cosh \left (c_1\right )-36}+\frac {18 x}{\sinh \left (c_1\right )+\cosh \left (c_1\right )-36}-\frac {8 \cosh \left (c_1\right )}{\sinh \left (c_1\right )+\cosh \left (c_1\right )-36}-\frac {8 \sinh \left (c_1\right )}{\sinh \left (c_1\right )+\cosh \left (c_1\right )-36}+\frac {294}{\sinh \left (c_1\right )+\cosh \left (c_1\right )-36}\right \},\left \{y(x)\to \frac {\sqrt {9 x^2 \sinh \left (c_1\right )+9 x^2 \cosh \left (c_1\right )-210 x \sinh \left (c_1\right )+6 x \sinh \left (2 c_1\right )-210 x \cosh \left (c_1\right )+6 x \cosh \left (2 c_1\right )+1225 \sinh \left (c_1\right )-70 \sinh \left (2 c_1\right )+\sinh \left (3 c_1\right )+1225 \cosh \left (c_1\right )-70 \cosh \left (2 c_1\right )+\cosh \left (3 c_1\right )}}{\sinh \left (c_1\right )+\cosh \left (c_1\right )-36}+\frac {18 x}{\sinh \left (c_1\right )+\cosh \left (c_1\right )-36}-\frac {8 \cosh \left (c_1\right )}{\sinh \left (c_1\right )+\cosh \left (c_1\right )-36}-\frac {8 \sinh \left (c_1\right )}{\sinh \left (c_1\right )+\cosh \left (c_1\right )-36}+\frac {294}{\sinh \left (c_1\right )+\cosh \left (c_1\right )-36}\right \}\right \}\] ✓ Maple : cpu = 0.152 (sec), leaf count = 51
\[ \left \{ y \left ( x \right ) ={\frac {9+ \left ( 3\,x+1 \right ) {{\it \_C1}}^{2}-6\,{\it \_C1}}{3\,{\it \_C1}}},y \left ( x \right ) =-2-2\,\sqrt {3\,x+1},y \left ( x \right ) =-2+2\,\sqrt {3\,x+1} \right \} \]