\[ (2-9 x) x^2 y''(x)^2+6 y(x) y''(x)-36 x y'(x)^2-6 (1-6 x) x y'(x) y''(x)=0 \] ✓ Mathematica : cpu = 0.0238162 (sec), leaf count = 24
DSolve[-36*x*Derivative[1][y][x]^2 + 6*y[x]*Derivative[2][y][x] - 6*(1 - 6*x)*x*Derivative[1][y][x]*Derivative[2][y][x] + (2 - 9*x)*x^2*Derivative[2][y][x]^2 == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {c_1{}^2 x^3}{c_2}+c_1 x+c_2\right \}\right \}\] ✓ Maple : cpu = 0.772 (sec), leaf count = 308
dsolve(x^2*(2-9*x)*diff(diff(y(x),x),x)^2-6*x*(1-6*x)*diff(y(x),x)*diff(diff(y(x),x),x)+6*diff(diff(y(x),x),x)*y(x)-36*x*diff(y(x),x)^2=0,y(x))
\[y \left (x \right ) = \frac {27 c_{1} \left (\left (9 x -1\right ) \sqrt {9}+9 \sqrt {9 x^{2}-2 x}\right )^{-\frac {5 \sqrt {9}}{18}} \sqrt {5}\, \sqrt {4}\, \sqrt {\frac {\frac {4}{5}+\frac {\sqrt {16}\, \left (x -\frac {1}{5}\right )}{\sqrt {9 x^{2}-2 x}}}{\sqrt {-\frac {\left (4 x -1\right )^{2}}{9 x^{2}-2 x}}}}\, \left (\left (9 x -1\right ) \sqrt {9}+9 \sqrt {9 x^{2}-2 x}\right )^{-\frac {2 \sqrt {9}}{9}} \sqrt {4 x -1}\, x \,{\mathrm e}^{-\frac {\sqrt {9 x^{2}-2 x}\, \left (\sqrt {16}-4\right )}{2}}}{4}\]