\[ (2-9 x) x^2 y''(x)^2+6 y(x) y''(x)-36 x y'(x)^2-6 (1-6 x) x y'(x) y''(x)=0 \] ✓ Mathematica : cpu = 0.0294689 (sec), leaf count = 24
\[\left \{\left \{y(x)\to \frac {c_1^2 x^3}{c_2}+c_1 x+c_2\right \}\right \}\]
✓ Maple : cpu = 0.634 (sec), leaf count = 308
\[ \left \{ y \left ( x \right ) =0,y \left ( x \right ) ={\frac {27\,{\it \_C1}\,\sqrt {5}\sqrt {4}x}{4} \left ( \left ( 9\,x-1 \right ) \sqrt {9}+9\,\sqrt {9\,{x}^{2}-2\,x} \right ) ^{-{\frac {2\,\sqrt {9}}{9}}} \left ( \left ( 9\,x-1 \right ) \sqrt {9}+9\,\sqrt {9\,{x}^{2}-2\,x} \right ) ^{-{\frac {5\,\sqrt {9}}{18}}}\sqrt {{1 \left ( {\frac {4}{5}}+{\sqrt {16} \left ( x-{\frac {1}{5}} \right ) {\frac {1}{\sqrt {9\,{x}^{2}-2\,x}}}} \right ) {\frac {1}{\sqrt {-{\frac { \left ( 4\,x-1 \right ) ^{2}}{9\,{x}^{2}-2\,x}}}}}}}\sqrt {4\,x-1}{{\rm e}^{-{\frac {-4+\sqrt {16}}{2}\sqrt {9\,{x}^{2}-2\,x}}}}},y \left ( x \right ) ={\frac {{\it \_C1}\,\sqrt {5}\sqrt {4}x}{135} \left ( \left ( 9\,x-1 \right ) \sqrt {9}+9\,\sqrt {9\,{x}^{2}-2\,x} \right ) ^{{\frac {2\,\sqrt {9}}{9}}} \left ( \left ( 9\,x-1 \right ) \sqrt {9}+9\,\sqrt {9\,{x}^{2}-2\,x} \right ) ^{{\frac {5\,\sqrt {9}}{18}}}\sqrt {4\,x-1}{{\rm e}^{{\frac {-4+\sqrt {16}}{2}\sqrt {9\,{x}^{2}-2\,x}}}}{\frac {1}{\sqrt {{1 \left ( {\frac {4}{5}}+{\sqrt {16} \left ( x-{\frac {1}{5}} \right ) {\frac {1}{\sqrt {9\,{x}^{2}-2\,x}}}} \right ) {\frac {1}{\sqrt {-{\frac { \left ( 4\,x-1 \right ) ^{2}}{9\,{x}^{2}-2\,x}}}}}}}}}},y \left ( x \right ) ={x}^{3}{\it \_C1}+{\it \_C2}\,x+{\frac {{{\it \_C2}}^{2}}{{\it \_C1}}} \right \} \]