Eigenvalue Of Fredholm Integral Equation

Question

How do I find Eigenvalue of Integral Equation

$y(x)= \lambda\int_{0}^{2\pi} sin(x)cos(t)y(t)dt$

I Dont know About Integral Equations, if anyone Help me to explain about how to approach such problem will be very much helpful

Answer 1

$y(x)= \lambda\int_{0}^{2\pi} sin(x)cos(t)dt$ is not an integral equation. It is a function:

$y(x)= \lambda \sin x \int_{0}^{2\pi} \cos(t)dt$

Since $\int_{0}^{2\pi} \cos(t)dt=0$, we have $y(x)=0$ for all $x$.