# Solve an integral equation in a shorter time

Consider the integral equation

$y(x)=x^3+\int _0^x\sin (x-t)y(t) dt$

Find the value of $y(1)$.

This is a Volterra I.E.I know that in order to solve it I will have to use the technique of Resolvent Kernel but that is very lengthy and it will surely take more than 15 mins to solve it.

I will have to appear in a competitive exam.Is there any easier way to solve this ?

• math.stackexchange.com/questions/139971/… can't you use this? (My suggestion may not be the optimal), and formulate it into Jordon canonical form. I suppose you could get your solution much faster. – Raaja Dec 5 '16 at 15:22