Question

please solve all 3 Differential Equation problems

3.8.7 Question Help Consider the following eigenvalue problem for which all of its eigenvalues are nonnegative y',thy-0; y(0)-0, y(1) + y'(1)-0 (a) Show that λ =0 is not an eigenvalue (b) Show that the eigenfunctions are the functions {sin α11,o, where αη įs the nth positive root of the equation tan z -z (c) Draw a sketch indicating the roots as the points of intersection of the curves y tan z and y -Z. Deduce from this sketch that an (2n-1/e n is large (a) Write the general solution when 0. y(x)- 3.8.1 Question Help * Find the values of λ eigenvalues for which the given problem has a nontrivial solution. Also determine the corresponding nontrivial solutions eigenfunctions =l land y =| |for n = 1 , 2, 3' 3.8.3 Question Help The eigenvalues in this problem are all nonnegative. First determine whether λ-0 is an eigenvalue; then find the positive eigenvalues and associated eigenfunctions. is λ = 0 an eigenvalue of this problem? Select the correct answer below and, if necessary, fill in the corresponding answer box to complete your choice. A. Yes, λ-0 is an eigenvalue with the corresponding eigenfunction yo(x)- B. No, when 0 the only solution to the given equation is the trivial solution. ° C. No, when λ = 0 there are an infinite number of nontrivial solutions to the give equation. What are the eigenvalues and eigenfunctions of the problem for n 1, 2, 3, .? Select the correct answer below and fill in the corresponding answer box to complete your choice. O A. The eigenvalues areThe eigenfunctions are yn(x)regardless of whether n is even or odd ○ B. The eigenvalues are λ-L. The eigenfunctions are yn(x)-D when n is even and yn (x)-L1 when n is odd.

Answer 1

tete a Selution

Ten inx) 万 13 are 3 and tha