4.185   ODE No. 1185

\[ \boxed { {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +5\,x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( 2\,{x}^{3}-4 \right ) y \left ( x \right ) =0} \]

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

Mathematica: cpu = 0.036005 (sec), leaf count = 67 \[ \left \{\left \{y(x)\to \frac {3 \sqrt [3]{6} c_2 K_0\left (\frac {2}{3} \sqrt {2} x^{3/2}\right )}{x^2}-\frac {3 \sqrt [3]{-3} c_1 I_0\left (\frac {2}{3} \sqrt {2} x^{3/2}\right )}{2^{2/3} x^2}\right \}\right \} \]

Maple: cpu = 0.016 (sec), leaf count = 35 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}}{{x}^{2}}{{\sl I}_{0 }\left ({\frac {2\,\sqrt {2}}{3}{x}^{{\frac {3}{2}}}}\right )}}+{\frac { {\it \_C2}}{{x}^{2}}{{\sl K}_{0}\left ({\frac {2\,\sqrt {2}}{3}{x}^{{ \frac {3}{2}}}}\right )}} \right \} \]