DIFFERENTIAL EQUATIONS - EXAMPLE 20.3 : A differential equation is given as y” + 5y’ + 6y = 0, y(0) = 2 and y’(0) = 3. By using Laplace transform, an engineer has correctly produced the equation L {y} = (2s + 13) / [(s + 2)(s + 3)] = A / (s + 2) + B (s + 3). (a) Find the values of A and B. (b) The inversed Laplace transform of 1 / (s + a) is given by exp (-at) where a is a constant. If the statement : L {y} = 9 L { exp (-2t) } - 7 L { exp (-3t) } is correct, find the equation of y as a function of t as a solution to the differential equation stated in the beginning of this question. When L {d} = 9 L {b} - 7 L {c}, then d = 9b - 7c with b, c and d are unknowns.
- 1 Answers
- 1436 Views
- I also Faced
- E-Mail Answers
Answer Posted / kangchuentat
DIFFERENTIAL EQUATIONS - ANSWER 20.3 : (a) Let (2s + 13) / [(s + 2)(s + 3)] = [A (s + 3) + B (s + 2)] / [(s + 2)(s + 3)]. Then 2s + 13 = As + 3A + Bs + 2B = (A + B)s + (3A + 2B), then A + B = 2 and 3A + 2B = 13. Let 2A + 2B = 4 as first equation by doubling A + B = 2 and 3A + 2B = 13 as second equation, the difference of first and second equations will produce A = 9. When A = 9, B = 2 - A = 2 - 9 = -7. (b) Let d = y, b = exp (-2t) and c = exp (-3t), then y = 9 exp (-2t) - 7 exp (-3t). The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
| Is This Answer Correct ? | 0 Yes | 0 No |
Post New Answer View All Answers
What is the maximum permissible Earth to Neutral voltage in an electrical system.
Explain the common failure mechanism for above ground atmospheric storage tanks?
what is first order of reaction?
PLEASE ANY ONE READ THIS MESSAGE ANSWER ME AT MY EMAIL ID surendrasaroj18@gmail.com sir i am prepairing for section engineer exam taken by railway my branch is chemical engineering i want previous paper of chemical engineering of section engineer exam taken by railway. please answer me as soon as possible thankyou
Explain why is post-weld heat treatment (stress relieving) sometimes necessary for welded vessels?
What is the easiest way to extract hydrogen from water and the safest way to store it?
Explain why is a vacuum breaker used on shell and tube heat exchangers that are utilizing steam as the heating utility?
What are the applications of screen analysis in the chemical industry?
What is a good source of equations for calculating discharge flowrates from accidental releases?
What is % of piping & equipment cost for a chemical plant having batch process?
Are there any general rules that should be considered when designing a slurry piping system?
If sum one has HAL placement paper plz mail me ,I m Chemical Engg.my id is er.kotnala@gmail.com
Hi, I am in need of interview questions from Engineers india limited in chemical engineering.if any one has kindly post it to me soon.
Do you have any idea on recombinant protein expression?
What are the different characteristics that can affect the flow of bulk solids and how?
