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The sequence (c, s, 1, [tex]e_1,\,e_{-1}[/tex]) is a basis for the solution space of some differential equation p(D)y = 0. Find this O.D.E.

NOTE: c = cos(t) and s = sin(t)

Work so far:

I know that [tex]e_1[/tex] gives a (t - 1) and that the [tex]e_{-1}[/tex] gives a (t + 1), but how do I solve for the 1! I think that the c and s give ([tex]t^2[/tex] - 1).

Also, can someone explain in detail or give a reference to what a Ker() is?

thanks

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# Homework Help: LINEAR ALGEBRA: Given a sequence as a basis for a solution of some O.D.E., find it

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