\[ \left (27 x^2+4\right ) y''(x)+27 x y'(x)-3 y(x)=0 \] ✓ Mathematica : cpu = 0.10836 (sec), leaf count = 103
DSolve[-3*y[x] + 27*x*Derivative[1][y][x] + (4 + 27*x^2)*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 \cosh \left (\frac {\sqrt {-27 x^2-4} \tan ^{-1}\left (\frac {3 x}{\sqrt {-9 x^2-\frac {4}{3}}}\right )}{3 \sqrt {27 x^2+4}}\right )+i c_2 \sinh \left (\frac {\sqrt {-27 x^2-4} \tan ^{-1}\left (\frac {3 x}{\sqrt {-9 x^2-\frac {4}{3}}}\right )}{3 \sqrt {27 x^2+4}}\right )\right \}\right \}\] ✓ Maple : cpu = 0.026 (sec), leaf count = 29
dsolve((27*x^2+4)*diff(diff(y(x),x),x)+27*x*diff(y(x),x)-3*y(x)=0,y(x))
\[y \left (x \right ) = c_{1} \sinh \left (\frac {\arcsinh \left (\frac {3 \sqrt {3}\, x}{2}\right )}{3}\right )+c_{2} \cosh \left (\frac {\arcsinh \left (\frac {3 \sqrt {3}\, x}{2}\right )}{3}\right )\]