Solving Integral Equation: sin(x)+∫_0^π sin(x-t)y(t)dt

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Homework Help Overview

The discussion revolves around solving the integral equation y(x) = sin(x) + ∫_0^π sin(x-t)y(t)dt, which falls under the subject area of integral equations and differential equations. Participants explore various methods to approach the problem, including differentiation and integration by parts.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss differentiating the equation to simplify it and explore the implications of doing so. There are attempts to apply integration by parts, with some questioning the validity of this approach. Others suggest using Laplace transforms or considering the nature of the integral limits.

Discussion Status

The discussion is active, with multiple participants contributing different methods and questioning each other's reasoning. Some participants have made progress in deriving expressions for y'(x) and y''(x), while others are still clarifying their understanding of the integration techniques and the implications of their calculations.

Contextual Notes

There are mentions of specific constraints, such as the limits of integration and the form of the integral equation, which influence the methods being considered. Participants also express uncertainty about how to derive initial conditions and evaluate integrals in the context of the problem.

  • #31
It's not Ax+B, it's f(x)=Aln(x)+B. You want to integrate ln(x/t)*f(t)=ln(x/t)*(Aln(t)+B)dt from t from 0 to 1. That breaks up into integrating ln(t)^2 and ln(t). Do them by integrating by parts. If you are having trouble with the individual integrations, it might be best to post a separate thread with your specific integration questions. This doesn't have much to do with integral equations.
 
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  • #32
Have you tried the laplace transform ... it applies very nicely here .:)

This equation is the Volterra integral equations .
 
  • #33
How does the Laplace trandform apply here?

Which integral equaiton is Volterra?
The ones are posted are Fredholm.
 

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