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1. Assume that the following initial value problem f′(t)2 + t = et−1, f(1) = 0.
has a unique solution f(t). Assume also that the solution can be expressed as a power series centred at t = 1
f(t) = a0 +a1(t−1)+a2(t−1)2 +a3(t−1)3 +a4(t−1)4 +... Find the first 2 non-zero terms of this series.
2. f and t are the first two none zero terms, what is my prize?
3. (Original post by bo0bo)
Assume that the following initial value problem f′(t)2 + t = et−1, f(1) = 0.
has a unique solution f(t). Assume also that the solution can be expressed as a power series centred at t = 1
f(t) = a0 +a1(t−1)+a2(t−1)2 +a3(t−1)3 +a4(t−1)4 +... Find the first 2 non-zero terms of this series.
(Original post by MyNameWasTaken12)
f and t are the first two none zero terms, what is my prize?
I have moved this to the correct forum for you
4. (Original post by bo0bo)
Assume that the following initial value problem f′(t)2 + t = et−1, f(1) = 0.
has a unique solution f(t). Assume also that the solution can be expressed as a power series centred at t = 1
f(t) = a0 +a1(t−1)+a2(t−1)2 +a3(t−1)3 +a4(t−1)4 +... Find the first 2 non-zero terms of this series.
You know that a_0 = f(1), a_1 = f'(1), a_2 = f''(1), etc... obviously a_0 = 0 from the given data so what about f'(1)?

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