4.274   ODE No. 1274

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

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

Mathematica: cpu = 0.043506 (sec), leaf count = 38 \[ \left \{\left \{y(x)\to c_1 \Gamma (1-v) J_{-v}\left (\sqrt {x}\right )+c_2 \Gamma (v+1) J_v\left (\sqrt {x}\right )\right \}\right \} \]

Maple: cpu = 0.0 (sec), leaf count = 19 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\sl J}_{v}\left (\sqrt {x} \right )}+{\it \_C2}\,{{\sl Y}_{v}\left (\sqrt {x}\right )} \right \} \]