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.
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 does the catalystic converter on an automobile really do?
If sum one has HAL placement paper plz mail me ,I m Chemical Engg.my id is er.kotnala@gmail.com
marketing procedure of iocl
What is the purpose of capacitor? What does capacitor load means? How does it connect?
What is a good relation to use for calculating tube bundle diameters?
What are the various utilities of the process plant?
What is maximum recommended velocity for steam in a plant pipe network?
What is the wet bulb globe temperature (wbgt)?
What is the import procurement cycle? What are the customization steps in sap?
how should i prepare for my placements.i am a student of chemical eng,final year,thapar university
what is the hearth and arch pressure in furnace?
Define "good" cooling tower water?
What are some good uses of low-grade steam at 12 atm and 1920c?
What are the specialized grinding methods?
How i can calculate heat transfer in reactor at unsteady state and what data should i have? I want equation and process to calculate it? As there is steam or brine in jacket