2.1483   ODE No. 1483

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

\[ (6 \nu +2 x-5) y'(x)-4 (\nu +x-1) y''(x)+(1-2 \nu ) y(x)+2 x y^{(3)}(x)=0 \] Mathematica : cpu = 0.114203 (sec), leaf count = 112

\[\left \{\left \{y(x)\to \frac {c_3 e^x x \Gamma \left (\frac {5}{2}-3 \nu \right ) \left (\frac {2 \, _1\tilde {F}_1\left (\frac {3}{2}-3 \nu ;1-2 \nu ;-x\right )}{3 (2 \nu -1) x}+\frac {2}{3 x \Gamma (2-2 \nu )}\right )}{\Gamma \left (\frac {3}{2}-\nu \right )}+c_2 e^x G_{2,3}^{2,1}\left (x\left |\begin {array}{c} 1,3 \nu -\frac {1}{2} \\ 1,2 \nu ,0 \\\end {array}\right .\right )+c_1 e^x\right \}\right \}\] Maple : cpu = 0.239 (sec), leaf count = 37

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