How Do You Convert Integral Equations into Initial Value Problems?

[potetochippu]

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

 

[MarneMath]

Think about the fundamental theorem of calculus. I think it'll become clearer once you look it over.

 

[Saitama]

I am not sure what you are asking about. Can you explain what is the meaning of "rewriting them as initial value problems"?

 

[HallsofIvy]

Differentiate both sides of the equation! What is y(1)?