for λ ∈ ℝ such that |λ| < \(\frac{5}{32}\), let R(x, t, λ) and u denote the resolvent kernel and the solution, respectively, of the Fredholm integral equation
\(\rm u(x)=x+\frac{\lambda}{2}\int_{-2}^2(xt+x^2t^2)u(t)dt\)
Then which of the following statements are true?
1
\(\rm R(x, t, \lambda )=\frac{3xt}{3-8\lambda}-\frac{5x^2t^2}{5-32\lambda}\)
2
\(\rm R(x, t, \lambda )=\frac{3xt}{3-8\lambda}+\frac{5x^2t^2}{5-32\lambda}\)
3
\(\rm u(1)=-\frac{5}{5-32\lambda}\)
4
\(\rm u(1)=\frac{3}{3-8\lambda}\)