2.1276   ODE No. 1276

\[ -4 e^x \sqrt {x^3}+4 x^2 y''(x)-\left (4 x^2+1\right ) y(x)+4 x y'(x)=0 \] Mathematica : cpu = 0.0296561 (sec), leaf count = 55


\[\left \{\left \{y(x)\to \frac {e^x \sqrt {x^3} (2 x-1)}{4 x^2}+\frac {c_1 e^{-x}}{\sqrt {x}}+\frac {c_2 e^x}{2 \sqrt {x}}\right \}\right \}\] Maple : cpu = 0.06 (sec), leaf count = 31


\[y \relax (x ) = \frac {\sinh \relax (x ) c_{2}}{\sqrt {x}}+\frac {\cosh \relax (x ) c_{1}}{\sqrt {x}}+\frac {\sqrt {x^{3}}\, {\mathrm e}^{x}}{2 x}\]