Show that the integral equation
x(t) = log(1 + t) + (1/5)(integral of e^(-t)cos^2(ts)(x(s))^2ds), integration going from 0 to 1
has a solution in C[0,1]. Justify your answer carefully.
Hint: Use the contraction mapping theorem. You may need to work with a suitable subset of C[0,1] rather than C[0,1]. Identifying such a subset is part of the problem.