2.1389   ODE No. 1389

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

\[ y''(x)=-\frac {y(x) \left (-4 n^2 x-v (v+1) (x-1)^2\right )}{4 (x-1)^2 x^2}-\frac {(3 x-1) y'(x)}{2 (x-1) x} \] Mathematica : cpu = 0.330181 (sec), leaf count = 217

\[\left \{\left \{y(x)\to c_2 (-1)^{\frac {1}{2} (-2 v-3)+1} x^{\frac {1}{4} (-2 v-3)+1} e^{\frac {1}{4} (-2 \log (1-x)-\log (x))} (x-1)^{\frac {1}{2} \left (n+\frac {1}{2} (2 n+1)+\frac {1}{2} (-2 v-3)+v+2\right )} \, _2F_1\left (\frac {1}{2} (2 n+1)+\frac {1}{2} (-2 v-3)+1,n+\frac {1}{2} (-2 v-3)+v+2;\frac {1}{2} (-2 v-3)+2;x\right )+c_1 x^{\frac {1}{4} (2 v+3)} e^{\frac {1}{4} (-2 \log (1-x)-\log (x))} (x-1)^{\frac {1}{2} \left (n+\frac {1}{2} (2 n+1)+\frac {1}{2} (-2 v-3)+v+2\right )} \, _2F_1\left (\frac {1}{2} (2 n+1),n+v+1;\frac {1}{2} (2 v+3);x\right )\right \}\right \}\] Maple : cpu = 0.124 (sec), leaf count = 68

\[\left \{y \left (x \right ) = \left (c_{1} x^{-\frac {v}{2}} \hypergeom \left (\left [-n -v , -n +\frac {1}{2}\right ], \left [-v +\frac {1}{2}\right ], x\right )+c_{2} x^{\frac {v}{2}+\frac {1}{2}} \hypergeom \left (\left [-n +v +1, -n +\frac {1}{2}\right ], \left [v +\frac {3}{2}\right ], x\right )\right ) \left (x -1\right )^{-n}\right \}\]