Consider the following initial value problem:0≤t≤7t>7y" + 25y =(7,10,y(0) = 7, y'(0) = 0Using Y for the Laplace transform of y(t), i.e., Y = L{y(t)}, find the equation youget by taking the Laplace transform of the differential equation and solve forY(s) =

We have to find the solution of the given initial value problem y" + 25y = 7, 0<t<7…

Answered: Consider the following initial value…

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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Use the Laplace transform to solve the following initial value problem: y" + 3y = 0 y(0) = 4, y(0) = 1 a. Using Y for the Laplace transform of y(t), i.e., Y = L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation = 0 b. Now solve for Y(s) = c. Write the above answer in its partial fraction decomposition, Y(s) = where a < b Y(s) = [ d. Now by inverting the transform, find y(t) = ■. A B s+a s+b Il+ +
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.
You 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 ost
Use Laplace Transforms to solve the following Differential Equation y" + 3y' + 2y = te' y(0) = y'(0) = 0 I|
Consider the following initial value problem: y" + 64y = 5t, 0≤t≤5 25, t> 5 3(0) = 0, 3/(0) = 0 Using Y for the Laplace transform of y(t), i.e., Y = C{y(t)}, find the equation you get by taking the Laplace transform of the differential equation and solve for Y(s) =
Q8
3. Use the Laplace transform to solve the given differential equation. x' - 2x - 4y = 4, y' + 2x + 2y = t, x(0) = 3, y(0) = 1. %3D
Q3 // Find the solution of the following Differential Equations using Laplace Transform properties; y" – 2y' - 3y = 0, where y(0) = 1 and y'(0) = 7 %3D
How would you solve the attached problem?
Use Laplace transform to solve the ordinary differential equation with discontinuous force. 3/" – 2y + 5y = { 10 sint : 0 27 y(7) = 1, y'(7) = 2e-" – 2

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Consider the following initial value problem: 0≤t≤7 t>7 y" + 25y = (7, 10, y(0) = 7, y'(0) = 0 Using Y for the Laplace transform of y(t), i.e., Y = L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation and solve for Y(s) =|