Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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- Consider the initial value problem y' + 3y = (b) Solve your equation for Y. Y = L {y} 0 11 0 (a) Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y by Y. Do not move any terms from one side of the equation to the other (until you get to part (b) below). = y = if 0 < t < 1 if 1 < t < 6 if 6 < t <∞, y(0) = 10. = (c) Take the inverse Laplace transform of both sides of the previous equation to solve for y.arrow_forwardYou have been provided with the following innitial value problem: Y"+16y= g(t), y(o)= 0, y'(0)=0 Where g(t)= ={t 't if 0 ≤ t <5 if 5≤ t ≤00 Apply the Laplace transform to both sides of the provided differential equation in order to derive the corresponding algebraic equation. Represent the Laplace transform of the function y(t) as Y(s). Avoid transferring terms between different sides of the equation until reaching part (b) as described below. Now solve the equation you found for Y(s): Y(s)=L{y(t)}= y(t)= Perform the inverse Laplace transform on both sides of the equation from the preceding step to find the solution for the function y(t).if need be, utilize h(t) to symbolize the Heaviside function: 0 if t ≤0 h(t)= If ostarrow_forwardHow would you solve the attached problem?arrow_forward
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