Consider the intial value problem:

, y(1) = 1, y'(1) = -1

a) Identify the coefficients of the Taylor Polynomial of order of 4 around by successive differentiation of the DE. State the resulting polynomial approximation to the solution,

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.