|Sep22-11, 05:00 PM||#1|
2nd basis function for 2nd order ODE
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!
|Sep23-11, 07:49 AM||#2|
found it, integral was a telescoping series from parts. the solution is \exp(-t)
|Sep23-11, 12:20 PM||#3|
Obviously, the second solution is exp(t)
|abels theorem, linear independent, odes|
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