Question

In: Math

Find the eigenvalues and eigenfunctions of the given boundary value problem. Assume that all eigenvalues are...

Find the eigenvalues and eigenfunctions of the given boundary value problem. Assume that all eigenvalues are real. (Let n represent an arbitrary positive number.)

y''+λy= 0,

y(0)= 0,

y'(π)= 0

Solutions

Expert Solution


Related Solutions

Find the eigenvalues λn and eigenfunctions yn(x) for the given boundary-value problem. (Give your answers in...
Find the eigenvalues λn and eigenfunctions yn(x) for the given boundary-value problem. (Give your answers in terms of k, making sure that each value of k corresponds to two unique eigenvalues.) y'' + λy = 0,  y(−π) = 0,  y(π) = 0 λ2k − 1 =, k=1,2,3,... y2k − 1(x) =, k=1,2,3,... λ2k =, k=1,2,3,... y2k(x) =, k=1,2,3,...
Find the eigenvalues λn and eigenfunctions yn(x) for the given boundary-value problem. (Give your answers in...
Find the eigenvalues λn and eigenfunctions yn(x) for the given boundary-value problem. (Give your answers in terms of n, making sure that each value of n corresponds to a unique eigenvalue.) y'' + λy = 0,  y(0) = 0,  y(π/6) = 0 λn =   , n = 1, 2, 3,    yn(x) =   , n = 1, 2, 3,   
Find the eigenvalues λn and eigenfunctions yn(x) for the given boundary-value problem. (Give your answers in...
Find the eigenvalues λn and eigenfunctions yn(x) for the given boundary-value problem. (Give your answers in terms of n, making sure that each value of n corresponds to a unique eigenvalue.) x2y'' + xy' + λy = 0,  y(1) = 0,  y'(e) = 0
Find the eigenvalues λn and eigenfunctions yn(x) for the given boundary-value problem. (Give your answers in...
Find the eigenvalues λn and eigenfunctions yn(x) for the given boundary-value problem. (Give your answers in terms of n, making sure that each value of n corresponds to a unique eigenvalue.) x2y'' + xy' + λy = 0,  y'(e−1) = 0,  y(1) = 0 λn = n = 1, 2, 3,    yn(x) = n = 1, 2, 3,   
Find the eigenfunctions for the following boundary value problem. x2y?? ? 15xy? + (64 + ?)?y...
Find the eigenfunctions for the following boundary value problem. x2y?? ? 15xy? + (64 + ?)?y ?=? 0,    y(e?1) ?=? 0, ?y(1) ?=? 0. In the eigenfunction take the arbitrary constant (either c1 or c2) from the general solution to be 1
Find the eigenvalues and eigenfunctions for the following boundary value problem. y"+6y'-(L-8)=0, y(0)=0, y(2)=0 L ==...
Find the eigenvalues and eigenfunctions for the following boundary value problem. y"+6y'-(L-8)=0, y(0)=0, y(2)=0 L == Lambda
Find the eigenvalues and eigenfunctions of the problem y" + λy = 0 , y(−π/2) =...
Find the eigenvalues and eigenfunctions of the problem y" + λy = 0 , y(−π/2) = 0 , y(π/2) = 0. Please explain in detail all steps. Thank you
Find the linear space of eigenfunctions for the problem with periodic boundary conditions u′′(x) = λu(x)...
Find the linear space of eigenfunctions for the problem with periodic boundary conditions u′′(x) = λu(x) u(0) = u(2π) u′(0) = u′(2π) for (a) λ = −1 (b) λ = 0 (c) λ = 1. Note that you should look for nontrivial eigenfunctions
Find eigenvalue (?) and eigenfunction and evaluate orthogonality from the given boundary value problem. ?2?′′ +...
Find eigenvalue (?) and eigenfunction and evaluate orthogonality from the given boundary value problem. ?2?′′ + ??′ + ?? = 0, ?(1) = 0, ?(5) = 0. Hint: Use Cauchy-Euler Equation, (textbook pp141-143).
(a) Find all positive values of λ for which the following boundary value problem has a...
(a) Find all positive values of λ for which the following boundary value problem has a nonzero solution. What are the corresponding eigenfunctions? X′′ + 4Xʹ + (λ + 4) X = 0, X′(0) = 0 and X′(1) = 0. Hint: the roots of its auxiliary equation are –2 ± σi, where λ = σ2. (b) Is λ = 0 an eigenvalue of this boundary value problem? Why or why not?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT