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Integral equation

$$y(x) = 1 + \lambda\int\limits_0^2\cos(x-t) y(t) \mathrm{d}t$$ has:

  1. a unique solution for $\lambda \neq \frac{4}{\pi +2}$;

  2. a unique solution for $\lambda \neq \frac{4}{\pi -2}$;

  3. no solution for $\lambda \neq \frac{4}{\pi +2}$, but the corresponding homogeneous equation has a non-trivial solution; or

  4. no solution for $\lambda \neq \frac{4}{\pi -2}$, but the corresponding homogeneous equation has a non-trivial solution.

I am stuck on this problem. Can anyone help me please?

  • 0
    If it is a question of some Indian Entrance Examination please add the source (Exam. name, year)in the title of this question. It will be helpful to other students using this site.2014-01-21

2 Answers 2