\[ \boxed { {x}^{2} \left ( 2-9\,x \right ) \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) ^{2}-6\,x \left ( 1-6\,x \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +6\, \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) y \left ( x \right ) -36\,x \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}=0} \]
Mathematica: cpu = 0.029004 (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 = 0.390 (sec), leaf count = 312 \[ \left \{ y \left ( x \right ) =27\,{\it \_C1}\, \left ( \left ( 9\,x-1 \right ) \sqrt {9}+9\,\sqrt {9\,{x}^{2}-2\,x} \right ) ^{-2/9\,\sqrt {9 }} \left ( \left ( 9\,x-1 \right ) \sqrt {9}+9\,\sqrt {x \left ( 9\,x-2 \right ) } \right ) ^{-{\frac {5\,\sqrt {9}}{18}}}\sqrt {{1 \left ( 1+1/ 2\,{\frac { \left ( -1/2+5/2\,x \right ) \sqrt {16}}{\sqrt {x \left ( 9\, x-2 \right ) }}} \right ) {\frac {1}{\sqrt {{\frac {-16\,{x}^{2}+8\,x-1 }{x \left ( 9\,x-2 \right ) }}}}}}}x\sqrt {4\,x-1}{{\rm e}^{2\,\sqrt {9 \,{x}^{2}-2\,x}-1/2\,\sqrt {16}\sqrt {x \left ( 9\,x-2 \right ) }}},y \left ( x \right ) ={\frac {{\it \_C1}\,x}{27} \left ( \left ( 9\,x-1 \right ) \sqrt {9}+9\,\sqrt {9\,{x}^{2}-2\,x} \right ) ^{{\frac {2\, \sqrt {9}}{9}}} \left ( \left ( 9\,x-1 \right ) \sqrt {9}+9\,\sqrt {x \left ( 9\,x-2 \right ) } \right ) ^{{\frac {5\,\sqrt {9}}{18}}}\sqrt {4 \,x-1}{{\rm e}^{-2\,\sqrt {9\,{x}^{2}-2\,x}+{\frac {\sqrt {16}}{2} \sqrt {x \left ( 9\,x-2 \right ) }}}}{\frac {1}{\sqrt {{1 \left ( 1+{ \frac {\sqrt {16}}{2} \left ( -{\frac {1}{2}}+{\frac {5\,x}{2}} \right ) {\frac {1}{\sqrt {x \left ( 9\,x-2 \right ) }}}} \right ) { \frac {1}{\sqrt {{\frac {-16\,{x}^{2}+8\,x-1}{x \left ( 9\,x-2 \right ) }}}}}}}}}},y \left ( x \right ) ={\it \_C1}\,{x}^{3}+{\it \_C2}\,x+{ \frac {{{\it \_C2}}^{2}}{{\it \_C1}}} \right \} \]