Answer to Question #251960 in Calculus for JaytheCreator

Question

Find the eigenvalues and the eigenfunctions of each of the following

(i) 𝑦 ′′ + 𝜆𝑦 = 0, 𝑦(0) = 0, 𝑦 ′ (𝑙) = 0,

(ii) 𝑦 ′′ + 𝜆𝑦 = 0, 𝑦(0) = 0, 𝑦(𝜋) − 𝑦 ′ (𝜋) = 0,

(iii) 𝑦 ′′ − 𝜆𝑦 = 0, 𝑦 ′ (0) = 0, 𝑦 ′ (𝑙) = 0.