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## Main Question or Discussion Point

Many of you have probably used the book Differential Equations by Lomen & Lovelock.

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:

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

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