Consider the intial value problem:

$\displaystyle x^2y''(x) - y(x) = 1 - x$, y(1) = 1, y'(1) = -1

a) Identify the coefficients of the Taylor Polynomial of order of 4 around $\displaystyle x_0 = 1$ by successive differentiation of the DE. State the resulting polynomial approximation to the solution, $\displaystyle T_4(x) = $

I've only had a one hour lecture on Taylor series solutions so I'm pretty new at this and have not had a non homogeneous problem before and also have not had one that was not centered at zero. If someone could give me a hint or maybe an example that would be awesome.