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
- 1412 Views
- I also Faced
- E-Mail Answers
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 |
Explain what are the problems that are associated with the expansion joints?
What are the different characteristics that can affect the flow of bulk solids and how?
What is the average salary for chemical engineers?
What is a common source of error in determining the percent spent caustic in refinery applications?
design calculations for reactor
Explain what are the advantages of using gear pumps?
How can I evaluate the thermal relief requirements for double block-in of 98% sulfuric acid?
Why does catalytic converter used in an automobile?
What significance the angle of repose holds in the chemical industry, explain?
Question 104 - In photoelectrical effect analysis of quantum chemistry, let E = kinetic energy of electron, p = intensity of UV light, f = frequency of UV light. According to Classical Theory, E = c for all values of f, E = mp. According to Quantum Theory, E = c for all values of p, E = mf + c. In a graph, m and c are constants where m is slope and c is y intercept. If m = 2 and c = 3 with similar value of E : (a) find the value of p according to Classical Theory; (b) find the value of f according to Quantum Theory.
How to calculate 40% of level in cylindrical vessel?
How 'saltation velocity' is used in designing pneumatic conveying systems?
-
Civil Engineering (5085) - Mechanical Engineering (4451)
- Electrical Engineering (16632)
- Electronics Communications (3918)
- Chemical Engineering (1095)
- Aeronautical Engineering (239)
- Bio Engineering (96)
- Metallurgy (361)
- Industrial Engineering (259)
- Instrumentation (3014)
- Automobile Engineering (332)
- Mechatronics Engineering (97)
- Marine Engineering (124)
- Power Plant Engineering (172)
- Textile Engineering (575)
- Production Engineering (25)
- Satellite Systems Engineering (106)
- Engineering AllOther (1379)
