Solve Impulse-Diffy eq. Homework: y''+y=δ(t-2π)cos(t), y(0)=0, y'(0)=1

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Homework Help Overview

The problem involves solving a second-order differential equation with a delta function and a cosine term, specifically y'' + y = δ(t - 2π)cos(t), with initial conditions y(0) = 0 and y'(0) = 1. The subject area is differential equations, particularly focusing on the application of Laplace transforms.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to manipulate the equation using Laplace transforms but expresses uncertainty about how to handle the product of the delta function and the cosine function. Some participants inquire about the integral form derived from the delta function and its implications.

Discussion Status

The discussion is ongoing, with participants exploring the implications of the delta function on the integral and clarifying the relevant topic area. There is an acknowledgment of the challenges posed by the delta function in this context, but no consensus has been reached on the next steps.

Contextual Notes

Participants are considering the role of the delta function in determining the bounds of the integral, indicating a potential area of confusion or exploration regarding its properties in the context of the problem.

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Homework Statement


y''+y=\delta (t-2\pi )cos(t)
y(0)=0,y'(0)=1


Homework Equations





The Attempt at a Solution


The left side is (s^2+1)Y(s)-1=RHS

My problem is the fact that cosine is being multiplied by the delta function. I put it in the form of an intergral but I don't know what to do from there.
 
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Well, good! Delta functions usually make integrals trivial. What integral did you get?
 
hmm, i don't know what is this question, may i know, what topic should i study for this question?
 
Differential Equations -Laplace transforms

OHHHH waitttt does the delta function just determine the bound of my intergral?
 

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