Here are the problems I am having difficulty with:

Given the characteristic equation of a 4th order differential equation has repeated roots of i and - i,

1.

a) write the general solution of the differential equation

b)write the original differential equation

$\displaystyle (x-2)y'' + (x-1)y' + 4y = 0$

2.

a) write the general solution near x = 0.

b) find the indicial equation and the exponents at the singularity.

Those are the 2 problems I am having trouble with. Its all just on how to start.. Here is what im am doing for each of them:

1.[/B]

A. I dont know how to do....

B.

$\displaystyle (m^2+2m+1)(m^2+2m+1)$

$\displaystyle y^(^4^) +4y''' + 6y'' + 4y' + 1 = 0$

With this you can just substitute

2.

$\displaystyle \sum Cn X^n$

where n = 0 to infinity and its appropriate derivatives. correct?