2nd basis function for 2nd order ODE

by X89codered89X
Tags: abels theorem, linear independent, odes
X89codered89X is offline
Sep22-11, 05:00 PM
P: 136
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!
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X89codered89X is offline
Sep23-11, 07:49 AM
P: 136
found it, integral was a telescoping series from parts. the solution is \exp(-t)
JJacquelin is offline
Sep23-11, 12:20 PM
P: 745
Obviously, the second solution is exp(t)

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