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The propagation of a wave u(x, t) in a long cable is described by the following initial value problem 6 UTM 0 u(x, 0) 4(2, 0)M UTM & UTM = e- 25- = COS T, where -o < x <0, and t > 0. Find the solution for this problem.

The propagation of a wave u(x, t) in a long cable is described by the following initial value problem 6 UTM 0 u(x, 0) 4(2, 0)M UTM & UTM = e- 25- = COS T, where -o < x <0, and t > 0. Find the solution for this problem.

Advanced Engineering Mathematics
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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Deffrential equation
UT (x, 0) = 0, UTM following initial value problem a) The propagation of a wave u(x, t) in a long cable is described by the UT 6 UTM UTM & L where -o < x < 0, and t > 0. Find the solution for this problem. = 25 u(x, 0) (2,0TM UTM UTM = e-x GUTM = COS Tx, M UTM b) Find the solution for the following wave equation IGUTM M G UTM 1 Utt UTM subject to the boundary conditions Uxx 4 0 < x < 4, t > 0, ITM UTM u(0, t) = 0, u(4, t) = 0, t > 0, and the initial conditions UTM UTM UTM $3 UTM u(r, 0) = (x – 1)², by using the method of separation of variables. UTM UTM UTM 0 < x < 4 UTM O UTM
Transcribed Image Text:UT (x, 0) = 0, UTM following initial value problem a) The propagation of a wave u(x, t) in a long cable is described by the UT 6 UTM UTM & L where -o < x < 0, and t > 0. Find the solution for this problem. = 25 u(x, 0) (2,0TM UTM UTM = e-x GUTM = COS Tx, M UTM b) Find the solution for the following wave equation IGUTM M G UTM 1 Utt UTM subject to the boundary conditions Uxx 4 0 < x < 4, t > 0, ITM UTM u(0, t) = 0, u(4, t) = 0, t > 0, and the initial conditions UTM UTM UTM $3 UTM u(r, 0) = (x – 1)², by using the method of separation of variables. UTM UTM UTM 0 < x < 4 UTM O UTM
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