Using the Laplace transform, obtain the solution r(t) of the Initial Value Problem(c) + x = 3 * u(t), where x(0)=1 and (0) = 1

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Answered: Using the Laplace transform, obtain the…

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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Using laplace transform , find the solution of the initial value problem (D² +5)y= cos(2x), where y(0)=0, y'(0)=0.
d Calculate ri(t) · r2(t)] and r1(t) × r2(t)] first by differentiating dt dt the product directly and then by applying the formulas d [ri(t) r2(t)] = ri(t) · dr2 + dt dri · r2(t) and %3| dt dt d dr2 dri [ri(t) x r2(t)] = r1(t) × x r2(t). dt + dt dt r1(t) = cos(t)i+ sin(t)j + 5tk, r2(t) = 4i + tk d dt d [ri(t) x r2(t)] : dt
Use the Fourier Transform Method to find the solution u(x,t) of the initial value problem: ut + tux 0, = with u(x, 0) = f(x), where the function f(x) is given by (1).
P.r
A) Find the Laplace transform of (2 03
Use the Laplace transform to solve the following initial value problem: x = 12x + 4y, y -8x + et X(s) Y(s) = = Let X(s) = L{x(t)}, and Y(s) = L{y(t)}. Find the expressions you obtain by taking the Laplace transform of both differential equations and solving for Y(s) and X(s): = x(t) y(t): = Find the partial fraction decomposition of X(s) and Y(s) and their inverse Laplace transforms to find the solution of the system of DES: = x(0) = 0, y(0)=0 =
Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function -4-5(t-1), (0)-6, (0) 0. = a Find the Laplace transform of the solution Y()-C (v(t)}- b. Obtain the solution y(t). (1) c Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at 1. if 0 < t < 1, -{₁ u(t)= if 1≤ t < 00.

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Using the Laplace transform, obtain the solution r(t) of the Initial Value Problem (c) + x = 3 * u(t), where x(0) = 1 and (0) = 1