(adsbygoogle = window.adsbygoogle || []).push({}); Volterra Eqn of 2nd Kind --> DEQ

1. The problem statement, all variables and given/known data

I need to convert y(x) = 1 - x + int[dt(x-t)y(t)] from 0 to x to a differential equation with the appropriate boundary conditions.

3. The attempt at a solution

OK I just had a problem converting a DEQ into an integral equation so I know the form it will take, I know it will be a 2nd order homogeneous equation... something like d^2y/dx^2 + y(x) = 0 with y(a) = b , dy/dx|c = d for some constants. I know it won't be a periodic boundary condition because that turns into a Fredholm Equation of the 2nd Kind.

So I applied d/dx to both sides getting

dy/dx = -1 + int[dty(t)] from 0 to x

I think this is valid since the integrand is with respect to t, I just applied the differentiation within the integral.

I'm not sure what to do from here though.

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# Volterra Eqn of 2nd Kind -> DEQ

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