\[ \boxed { 4\,{x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +4\,x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( 4\,{x}^{2}+1 \right ) y \left ( x \right ) -4\,\sqrt {{x}^{3}}{{\rm e}^{x}}=0} \]
Mathematica: cpu = 0.046506 (sec), leaf count = 55 \[ \left \{\left \{y(x)\to \frac {c_1 e^{-x}}{\sqrt {x}}+\frac {c_2 e^x}{2 \sqrt {x}}+\frac {e^x \sqrt {x^3} (2 x-1)}{4 x^2}\right \}\right \} \]
Maple: cpu = 0.063 (sec), leaf count = 31 \[ \left \{ y \left ( x \right ) ={\sinh \left ( x \right ) {\it \_C2}{\frac {1}{\sqrt {x}}}}+{\cosh \left ( x \right ) {\it \_C1}{\frac {1}{\sqrt {x }}}}+{\frac {{{\rm e}^{x}}}{2\,x}\sqrt {{x}^{3}}} \right \} \]