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2nd basis function for 2nd order ODE 
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#1
Sep2211, 05:00 PM

P: 137

i have the first solution y_1(t) = t for (1t)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
Sep2311, 07:49 AM

P: 137

found it, integral was a telescoping series from parts. the solution is \exp(t)



#3
Sep2311, 12:20 PM

P: 756

Obviously, the second solution is exp(t)



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