Register to reply

2nd basis function for 2nd order ODE

by X89codered89X
Tags: abels theorem, linear independent, odes
Share this thread:
X89codered89X
#1
Sep22-11, 05:00 PM
P: 140
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!
Phys.Org News Partner Science news on Phys.org
What lit up the universe?
Sheepdogs use just two simple rules to round up large herds of sheep
Animals first flex their muscles
X89codered89X
#2
Sep23-11, 07:49 AM
P: 140
found it, integral was a telescoping series from parts. the solution is \exp(-t)
JJacquelin
#3
Sep23-11, 12:20 PM
P: 759
Obviously, the second solution is exp(t)


Register to reply

Related Discussions
2nd ODE, Reduction of Order, Basis known Differential Equations 2
Basis in function space Linear & Abstract Algebra 1
Twoness: A Theory for the Basis of Order found in Ancient Wisdom General Discussion 82
Basis function method Quantum Physics 5
The Basis of Order General Discussion 34