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For my class I'm working on Example 2, Page 153.

You don't need to see the book, though, to help me out. It's a four-part problem and I'm on the last step not knowing where to take it.

In Part B, we created a DE:

dP/dt = (397/4169) P + (6580236/4169)

and solved it:

P(t) = (397/8338) t^2 + (6580236/4169) t + (1225953/4169)

Now in Part D they ask:

**"Expand the explicit solution you obtained in Part B in a Taylor Series about the origin."**I'm not so sure I've ever done anything like this, so I'm not clear on what steps I should take. I believe my teacher said I should find a similar Taylor Series and manipulate it to fit my needs but that still doesn't get me very far.

Absolutely any insight is appreciated, hope you can help me!

Thanks,

Eric