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.