x1X2I3Solve the following initial value problem:ddt3 -1 6-CD-~-0-5 7 6 I, (0) =1 -1 8x =

According to the given data, find the general solution.

Answered: Solve the following initial value…

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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2. A bacteria culture starts with 10,000 bacteria and the number doubles every 40 minutes. Determine a formula for the number of bacteria at time t. A. f(t) = 10,000 x 20.5t ; where t is the number of hours B. f(t) = 10,000 x 21.5t ; where t is the number of hours C. f(t) = 10,000 x 2t ; where t is the number of hours
Let us revisit a question from a few problem sets ago with slightly different numbers. A patient takes 200 mg of an antibiotic every 6 hours. The half-life of the drug (the time it takes for half of the drug to be eliminated from the blood) is 6 hours. Let dn denote the amount (in mg) of medication in the bloodstream after n doses, where d₁= 200. 1. Explain why dn+1 = 0.5dn + 200, d₁= 200 is the correct recurrence relation. 2. Use the recurrence relation to write down the expressions for d2, d3, and d4. Do not simplify- instead, keep powers of 0.5 in your answers. 3. You should see that each dn is a geometric sum. We are interested in finding the long-term (steady state) amount of antibiotic in your blood, i.e., limno dn. Write this limit as an infinite series using summation (E) notation. 4. Evaluate the geometric series from the previous part using the geometric series formula. 5. Previously we used the recurrence relation dn+1 = 0.5dn + 200, d₁ = 200 and the assumption that dn→ L to…
3. 1 19 11 8 =51 8 2] 55 41[2 X8 2 5]l1 7 [18 B- Find the Value of X :- 1 89 59 [2 6 157 66 60
I would like an explanation for this question.

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Solve the following initial value problem: 3 -1 6 4-09---0 ) = -5 7 6, 7(0) = 1 -1 8 d dt