2.1496   ODE No. 1496

\[ a x^2 y(x)+x^2 y^{(3)}(x)+6 x y''(x)+6 y'(x)=0 \] Mathematica : cpu = 0.194448 (sec), leaf count = 63


\[\left \{\left \{y(x)\to \frac {c_1 e^{-\sqrt [3]{a} x}}{x^2}+\frac {c_2 e^{\sqrt [3]{-1} \sqrt [3]{a} x}}{x^2}+\frac {c_3 e^{-(-1)^{2/3} \sqrt [3]{a} x}}{x^2}\right \}\right \}\] Maple : cpu = 0.03 (sec), leaf count = 57


\[y \relax (x ) = \frac {c_{1} {\mathrm e}^{\frac {\left (-a \right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right ) x}{2}}+c_{2} {\mathrm e}^{-\frac {\left (-a \right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right ) x}{2}}+c_{3} {\mathrm e}^{\left (-a \right )^{\frac {1}{3}} x}}{x^{2}}\]