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( Find the general solution to the homogeneous differential equation The solution has the form d²y dt² - dy 12- + 100y = 0 dt y = C₁f₁(t) + C₂f₂(t) with f₁(t) = f₂ (t) = Left to your own devices, you will probably write down the correct answers, but in case you want to quibble, enter your answers so that the functions are normalized with their values at t = 0 equal to 0 and 1(respectively), and they are expressed as simply as possible. and

( Find the general solution to the homogeneous differential equation The solution has the form d²y dt² - dy 12- + 100y = 0 dt y = C₁f₁(t) + C₂f₂(t) with f₁(t) = f₂ (t) = Left to your own devices, you will probably write down the correct answers, but in case you want to quibble, enter your answers so that the functions are normalized with their values at t = 0 equal to 0 and 1(respectively), and they are expressed as simply as possible. and

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Find the general solution to the homogeneous differential equation d²y dt² The solution has the form dy - - 12- + 100y = 0 dt y = C₁f₁(t) + C₂f2(t) with f₁(t) = f₂(t) = Left to your own devices, you will probably write down the correct answers, but in case you want to quibble, enter your answers so that the functions are normalized with their values at t = 0 equal to 0 and 1(respectively), and they are expressed as simply as possible. and
Transcribed Image Text:Find the general solution to the homogeneous differential equation d²y dt² The solution has the form dy - - 12- + 100y = 0 dt y = C₁f₁(t) + C₂f2(t) with f₁(t) = f₂(t) = Left to your own devices, you will probably write down the correct answers, but in case you want to quibble, enter your answers so that the functions are normalized with their values at t = 0 equal to 0 and 1(respectively), and they are expressed as simply as possible. and
2" (5n) n=15 (a) Find the ratio of successive terms. Write your answer as a fully simplified fraction. For n ≥ 15, ..) Use the ratio test to determine whether an+1 lim n→∞0 an = lim n→ ∞ lim 12-00 an (b) Evaluate the limit in the previous part. Enter ∞ as infinity and coas -infinity. If the limit does not exist, enter DNE. an+1 converges or diverges. = (c) By the ratio test, does the series converge, diverge, or is the test inconclusive? Choose
Transcribed Image Text:2" (5n) n=15 (a) Find the ratio of successive terms. Write your answer as a fully simplified fraction. For n ≥ 15, ..) Use the ratio test to determine whether an+1 lim n→∞0 an = lim n→ ∞ lim 12-00 an (b) Evaluate the limit in the previous part. Enter ∞ as infinity and coas -infinity. If the limit does not exist, enter DNE. an+1 converges or diverges. = (c) By the ratio test, does the series converge, diverge, or is the test inconclusive? Choose
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