\[ 16 x^2 y''(x)+(4 x+3) y(x)=0 \] ✓ Mathematica : cpu = 0.0251443 (sec), leaf count = 47
\[\left \{\left \{y(x)\to c_1 e^{i \sqrt {x}} \sqrt [4]{x}+i c_2 e^{-i \sqrt {x}} \sqrt [4]{x}\right \}\right \}\] ✓ Maple : cpu = 0.022 (sec), leaf count = 21
\[y \relax (x ) = x^{\frac {1}{4}} \left (\cos \left (\sqrt {x}\right ) c_{2}+\sin \left (\sqrt {x}\right ) c_{1}\right )\]