\[ (2-9 x) x^2 y''(x)^2+6 y(x) y''(x)-36 x y'(x)^2-6 (1-6 x) x y'(x) y''(x)=0 \] ✓ Mathematica : cpu = 0.0270212 (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 = 0.542 (sec), leaf count = 312
\[ \left \{ y \left ( x \right ) =27\,{\it \_C1}\, \left ( \left ( 9\,x-1 \right ) \sqrt {9}+9\,\sqrt { \left ( 9\,x-2 \right ) x} \right ) ^{-{\frac {5\,\sqrt {9}}{18}}}\sqrt {{1 \left ( 1/2\,{\frac { \left ( -1/2+5/2\,x \right ) \sqrt {16}}{\sqrt { \left ( 9\,x-2 \right ) x}}}+1 \right ) {\frac {1}{\sqrt {{\frac {-16\,{x}^{2}+8\,x-1}{ \left ( 9\,x-2 \right ) x}}}}}}} \left ( \left ( 9\,x-1 \right ) \sqrt {9}+9\,\sqrt {9\,{x}^{2}-2\,x} \right ) ^{-2/9\,\sqrt {9}}\sqrt {4\,x-1}x{{\rm e}^{-1/2\,\sqrt {16}\sqrt { \left ( 9\,x-2 \right ) x}+2\,\sqrt {9\,{x}^{2}-2\,x}}},y \left ( x \right ) ={\frac {{\it \_C1}\,x}{27} \left ( \left ( 9\,x-1 \right ) \sqrt {9}+9\,\sqrt { \left ( 9\,x-2 \right ) x} \right ) ^{{\frac {5\,\sqrt {9}}{18}}} \left ( \left ( 9\,x-1 \right ) \sqrt {9}+9\,\sqrt {9\,{x}^{2}-2\,x} \right ) ^{{\frac {2\,\sqrt {9}}{9}}}\sqrt {4\,x-1}{{\rm e}^{{\frac {\sqrt {16}}{2}\sqrt { \left ( 9\,x-2 \right ) x}}-2\,\sqrt {9\,{x}^{2}-2\,x}}}{\frac {1}{\sqrt {{1 \left ( {\frac {\sqrt {16}}{2} \left ( -{\frac {1}{2}}+{\frac {5\,x}{2}} \right ) {\frac {1}{\sqrt { \left ( 9\,x-2 \right ) x}}}}+1 \right ) {\frac {1}{\sqrt {{\frac {-16\,{x}^{2}+8\,x-1}{ \left ( 9\,x-2 \right ) x}}}}}}}}}},y \left ( x \right ) ={x}^{3}{\it \_C1}+{\it \_C2}\,x+{\frac {{{\it \_C2}}^{2}}{{\it \_C1}}} \right \} \]