Use Inverse Laplace Transform method and another method to find the partial solution of
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Use Inverse Laplace Transform method and another method to find the partial solution of s y...
1.Find the inverse Laplace transform 2. Use the method of variation of parameters to find the general solution of the system e -TTS F(s) = s(S2 + 1) x'= ( 2.)x+{2}') = Ax+ g(0)
Question 1: [25 pts] S+1 a) Find the inverse Laplace transform of the expression $2+4 b) Find the inverse Laplace transform of the expression (s-5)(s2+4) c) Use the information from the parts a) and b) to find the solution of the IVP y" + 4y = 6e5t, y(0) = 1, y'(0) = 1.
Use the Laplace Transform method to solve the IVP y" - 8y + 16y = t4 y(0) = 1,5(0) - 4. Show all your work Note: A partial fraction decomposition will not be needed here if you carefully solve for Y(s) = {y}(s), by first moving the expression of the form -as - b with a and b positive integers to the right hand side and then dividing both sides of the equation by the coefficient of Y() which will...
Question 4 Use the method of Laplace transform to find the solution of the initial value problem Zy" + y' + 4-2 δ(t-r/6) sint, y'(0)-0. y(0)-0, Solution: Question 4 Use the method of Laplace transform to find the solution of the initial value problem Zy" + y' + 4-2 δ(t-r/6) sint, y'(0)-0. y(0)-0, Solution:
Page 2 II. (7) Use the Laplace Transform method to solve the IVP y' - 8y + 16y = 14 y(0) = 1,5/(0) = 4 Show all your work. Note: A partial fraction decomposition will not be needed here if you carefully solve for Y (s) = {y}(s), by first moving the expression of the form -as - b with a and b positive integers to the right hand side and then dividing both sides of the equation by the...
Use partial fraction to evaluate inverse Laplace Transform of S- 1 F(s) = (s + 1)(s + 2)
Problem 1: Find the Laplace transform X(s) of x(0)-6cos(Sr-3)u(t-3). 10 Problem 2: (a) Find the inverse Laplace transform h() of H(s)-10s+34 (Hint: use the Laplace transform pair for Decaying Sine or Generic Oscillatory Decay.) (b) Draw the corresponding direct form II block diagram of the system described by H(s) and (c) determine the corresponding differential equation. Problem 3: Using the unilateral Laplace transform, solve the following differential equation with the given initial condition: y)+5y(0) 2u), y(0)1 Problem 4: For the...
Use the method of completing the square to find the partial fraction expansion and inverse transform. F(s) = (s+4)/(s^3+4*s^2+s)
(1 point) Use the Laplace transform to solve the following initial value problem x, = 10x + 4y, y=-6x + e4, x(0) = 0, y(0) = 0 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): S)E Y(s) = Find the partial fraction decomposition of X(s) and Y(s) and their inverse Laplace transforms to find the solution of the...
3. Find the inverse Laplace transform of F(s)- 3. Find the inverse Laplace transform of F(s)-