2. Solve the differential equation(a) x" + 6x' + 10x = 0(c) x" + 25x = 0.(e) x + 2x" + x = 0(b) x'" - 4x" + 13x' = 0.(d) x'"' +7x" = 0(f) x'" - 16x= :0(g) (D+1)²(D² + 1) (D² - 2D + 5)²x = 0(h) D² (D – 5)³(D² +16)² (D² +8D+25)x = 0

Answered: Image /qna-images/answer/9ed37db0-1d79-4055-8dc2-3ae697fd8772.jpg

Answered: 2. Solve the differential equation (a)…

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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(6) A bacterial culture contains y(0) grown to y(2) = 250[cells]. Construct and solve the differential equation assuming exponential growth. Determine the number of cells y(t) as a function of time. After how many hours does the bacterial culture 50[cells] at t O[hr]. After t = 2[hr], the bacterial culture has contain 2000 cells?
Can you help me solve the differential equation?
A biologist is tracking Lyme Disease cases in a deer population of 8500 in a state forest in Wisconsin. Suppose at time t = 0 the number D(t) of deer with Lyme Disease is 2250 and is increasing at a rate of 110 deer per month. Assume that D'(t) is proportional to the product of the number of deer who have caught Lyme's disease and of those who have not. (a) Write a differential equation to represent this scenario. Use k for your proportionality constant and D(t) as your function (not D). D'(t) kD(t) (8500 – D(t)) ✓ os = می (b) If you did part (a) correctly, the general solution to your differential equation is D(t) = 8500 1+ Ce-8500kt Find C (keep C exact). C = 25 9 من (c) Find k. (Hint: you do NOT need the function in part (b) to find k). Keep k exact. k 1 125000 (d) How long will it take for 50% of the deer population to develop Lyme Disease? Keep k and C exact until your final calculation. Round your final answer to two decimal places. 13.59 ✓ months
(1) Solve x'= 2. -36
As a salt dissolves in methanol, the number x(t) of grams of the salt in a solution after t seconds satisfies the dx differential equation =1.6x-0.004x² (a) What is the maximum amount of the salt that will ever dissolve in the methanol? (b) If x=50 when t=0, how long will it take for an additional 50 g of salt to dissolve? (a) The maximum amount of the salt that will ever dissolve in the methanol is gijams. (Simplify your answer.) 5 AI 9 IN F5 F6 2 8 # B - U dt F7 → = ∞ A View an example Get more help. ↓ F8 H i 8 ↑ 2 e B F9 ↑ T' l Y F10 + + 1 8 *** F11 √i co Less F12 ● S Vi 2 Ө ÷ 1, A = Clear all L PRISC INS X U SCRLK - O HOME C V € Σ PAUSE PG UP 8 FR v -W. Check answer NUM (88) A S i x

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2. Solve the differential equation (a) x" + 6x' + 10x = 0 (c) x" + 25x = 0. - (e) x + 2x" + x = 0 (b) x'"- 4x" + 13x' = 0. +7x"=0 (d) x' (f) x - 16x = 0 (g) (D+1)²(D² + 1) (D² - 2D + 5)²x = 0 (h) D² (D – 5)³ (D² +16)² (D² +8D+25)x = 0