How Do You Convert Integral Equations into Initial Value Problems?

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Homework Help Overview

The discussion revolves around converting an integral equation into an initial value problem, specifically focusing on the equation y(x) = 2 + ∫(y(t))^2dt from 1 to x.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the fundamental theorem of calculus as a potential guiding principle. There are questions regarding the meaning of "rewriting them as initial value problems" and suggestions to differentiate both sides of the equation.

Discussion Status

The discussion is in an exploratory phase, with participants offering guidance and raising questions. Some have provided hints about differentiation and the fundamental theorem, while others seek clarification on the problem's requirements.

Contextual Notes

The original poster expresses uncertainty due to a lack of coverage on the topic in their textbooks and difficulty finding examples online.

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Homework Statement


Solve the following integrale equation by rewriting them as initial value problems:

y(x) = 2 + ∫(y(t))^2dt -this is a definite integral with limits from 1 to x


Homework Equations





The Attempt at a Solution



I am unsure how to approach this question at all because my textbooks did not cover this topic and I couldn't find any examples on the internet either. Thanks
 
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Think about the fundamental theorem of calculus. I think it'll become clearer once you look it over.
 
I am not sure what you are asking about. Can you explain what is the meaning of "rewriting them as initial value problems"?
 
Differentiate both sides of the equation! What is y(1)?
 

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