Which of the following options correctly solves the integral equation y^(')(t)+\int_0^t y(\lambda )cos(t-\lambda
)d\lambda =cos(t) with the initial condition y(0)=0?

A) y(t) = cos(t)
B) y(t) = sin(t)
C) y(t) = -sin(t)
D) y(t) = 1-cos(t)