How does one formulate this integral equation as an initial value problem?

u(t)=1 + integral from 0 to t (s ln (s/t) u(s) ds)

we're supposed to use Leibniz formula but I'm not sure how to apply it. Thanks!

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- May 10th 2011, 03:22 PMmorganforIVP using Leibniz formula
How does one formulate this integral equation as an initial value problem?

u(t)=1 + integral from 0 to t (s ln (s/t) u(s) ds)

we're supposed to use Leibniz formula but I'm not sure how to apply it. Thanks! - May 10th 2011, 07:23 PMAckbeet
So your integral equation is

and you need to convert to an IVP using the Leibniz formula, which is, in this case,

So, why not just differentiate the original integral equation with respect to t, and use the Leibniz formula on the integral. What do you get? - May 10th 2011, 11:10 PMDrexel28
- May 11th 2011, 02:41 AMAckbeet