Hi guys I am currently stuck at a question.

i) Show that if

satisfies the integral equation

then

is a solution to the initial value problem

for

, with

ii) Prove the converse of the result in part (i).

(Hint: You will need to do a change of order of integration in a double integral.)

Part (i) I differentiated

twice and got the result by applying Leibniz rule and the fundamental theorem of calculus.

For part (ii) I don't even know where to start. Where would I be using a double integral? I tried proving it just by integrating

but I wasn't sure if i could do that.

Any help would be appreciated.

Thanks.