\[ -4 e^x \sqrt {x^3}+4 x^2 y''(x)-\left (4 x^2+1\right ) y(x)+4 x y'(x)=0 \] ✓ Mathematica : cpu = 0.0296561 (sec), leaf count = 55
DSolve[-4*E^x*Sqrt[x^3] - (1 + 4*x^2)*y[x] + 4*x*Derivative[1][y][x] + 4*x^2*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {e^x \sqrt {x^3} (2 x-1)}{4 x^2}+\frac {c_1 e^{-x}}{\sqrt {x}}+\frac {c_2 e^x}{2 \sqrt {x}}\right \}\right \}\] ✓ Maple : cpu = 0.06 (sec), leaf count = 31
dsolve(4*x^2*diff(diff(y(x),x),x)+4*x*diff(y(x),x)-(4*x^2+1)*y(x)-4*(x^3)^(1/2)*exp(x)=0,y(x))
\[y \left (x \right ) = \frac {\sinh \left (x \right ) c_{2}}{\sqrt {x}}+\frac {\cosh \left (x \right ) c_{1}}{\sqrt {x}}+\frac {\sqrt {x^{3}}\, {\mathrm e}^{x}}{2 x}\]