2nd basis function for 2nd order ODE

  1. i have the first solution y_1(t) = t for (1-t)y'' + ty' - y = 0.

    I need to get the 2nd linearly independent using Abels theorem.

    the integration is messy but i have it set up (sorry no latex);

    y_2 = (t) * integral to t ( 1/s^2 * exp( -integral to t (s(s+1) ds) ) ds.

    Could anyone show me how to do this integration step by step?

    Thanks in advance!
  2. jcsd
  3. found it, integral was a telescoping series from parts. the solution is \exp(-t)
  4. Obviously, the second solution is exp(t)
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