2.1483   ODE No. 1483

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

\[ -4 (\nu +x-1) y''(x)+(6 \nu +2 x-5) y'(x)+(1-2 \nu ) y(x)+2 x y^{(3)}(x)=0 \] Mathematica : cpu = 0.149599 (sec), leaf count = 105

\[\left \{\left \{y(x)\to e^x \left (\frac {2 c_3 \Gamma \left (\frac {5}{2}-3 \nu \right ) \left (\Gamma (2-2 \nu ) \, _1\tilde {F}_1\left (\frac {3}{2}-3 \nu ;1-2 \nu ;-x\right )+2 \nu -1\right )}{3 (2 \nu -1) \Gamma (2-2 \nu ) \Gamma \left (\frac {3}{2}-\nu \right )}+c_2 G_{2,3}^{2,1}\left (x\left |\begin {array}{c} 1,3 \nu -\frac {1}{2} \\ 1,2 \nu ,0 \\\end {array}\right .\right )+c_1\right )\right \}\right \}\]

Maple : cpu = 0.273 (sec), leaf count = 37

\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{x}}+{\it \_C2}\,{{\rm e}^{{\frac {x}{2}}}}{x}^{\nu }{{\sl I}_{\nu }\left ({\frac {x}{2}}\right )}+{\it \_C3}\,{{\rm e}^{{\frac {x}{2}}}}{x}^{\nu }{{\sl K}_{\nu }\left ({\frac {x}{2}}\right )} \right \} \]