1a) Using Laplace transforms solve the following differential equation:d²y(t)dy(t)+ + 2y(t) = e-t,dt²dtsubject to the initial conditionsy(0) = 0 and dy (0)= 1.dtA table of Laplace transforms is provided at the end of the paper.b) A periodic function f(t) with period T = 2π is defined as:f(t) = {t, for 0≤t≤n10 for ≤t≤0Find the Fourier series expansion of f(t). (Hint: Use integration by parts).

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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 transforms solve the following differential equation: d²y(t) dy(t) + + 2y(t) = e-t, dt² dt subject to the initial conditions y (0) = 0 and dy(0) = 1. dt A table of Laplace transforms is provided at the end of the paper.