Question

For what values of a (if any) does the boundary value problem x'' + ax =...

For what values of a (if any) does the boundary value problem
x'' + ax = 0, x(0) = 0, x(π) = 0
have nontrivial (i.e. nonzero) solutions

Hint: In order to solve, divide the problem into three cases
1. If a > 0. In this case let a = b^2. 2. If a < 0. In this case let a = −b^2. 3. If a = 0.

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

if you have any problem understanding the solution please leave a comment.

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
For what values of a (if any) does the boundary value problem x'' + ax' =...
For what values of a (if any) does the boundary value problem x'' + ax' = 0, x(0) = 0, x(π) = 0 have nontrivial (i.e. nonzero) solutions Hint: In order to solve, divide the problem into three cases 1. If a > 0. In this case let a = b^2. 2. If a < 0. In this case let a = −b^2. 3. If a = 0.
Solve the given boundary-value problem. y'' − 2y' + 2y = 2x − 2,   y(0) =...
Solve the given boundary-value problem. y'' − 2y' + 2y = 2x − 2,   y(0) = 0, y(π) = π
Find all eigenvalues and corresponding eigenfunctions for the following boundary value problem (x^2)y'' + λy =...
Find all eigenvalues and corresponding eigenfunctions for the following boundary value problem (x^2)y'' + λy = 0, (1 < x < 2), y(1) = 0 = y(2) and in particular the three cases μ < 1/2, μ = 1/2, and μ > 1/2 associated with the sign and vanishing of the discriminant of the characteristic equation
Solve the following initial/boundary value problem: ∂u(t,x)/∂t = ∂^2u(t,x)/∂x^2 for t>0, 0<x<π, u(t,0)=u(t,π)=0 for t>0, u(0,x)=sin^2x...
Solve the following initial/boundary value problem: ∂u(t,x)/∂t = ∂^2u(t,x)/∂x^2 for t>0, 0<x<π, u(t,0)=u(t,π)=0 for t>0, u(0,x)=sin^2x for 0≤x≤ π. if you like, you can use/cite the solution of Fourier sine series of sin^2(x) on [0,pi] = 1/4-(1/4)cos(2x) please show all steps and work clearly so I can follow your logic and learn to solve similar ones myself.
Solve the given initial-value problem in which the input function g(x) is discontinuous. [Hint: Solve the...
Solve the given initial-value problem in which the input function g(x) is discontinuous. [Hint: Solve the problem on two intervals, and then find a solution so that y and y' are continuous at x = π/2.] y'' + 4y = g(x),   y(0) = 1, y'(0) = 3,   where g(x) = sin(x),    0 ≤ x ≤ π/2 0,    x > π/2 Find y(x) for each of the intervals.   ,    0 ≤ x ≤ π/2   ,    x > π/2
Solve the given initial-value problem. (Enter the first three nonzero terms of the solution.) (x +...
Solve the given initial-value problem. (Enter the first three nonzero terms of the solution.) (x + 2)y'' + 3y = 0,  y(0) = 0,  y'(0) = 1
Find u(x,y) harmonic in S with given boundary values: S = {(x,y): 1 < y <...
Find u(x,y) harmonic in S with given boundary values: S = {(x,y): 1 < y < 3} , u(x,y) = 5 (if y=1) and = 7 (when y=3) I have this problem to solve, and I'm not sure where to start. Any help would be appreciated. Thanks!
solve the boundary value problem: y''(x)+y(x)=e^x for 0<x<pi with y(0)=0 and y(pi)+y'(pi)=0. please show all steps.
solve the boundary value problem: y''(x)+y(x)=e^x for 0<x<pi with y(0)=0 and y(pi)+y'(pi)=0. please show all steps.
Prepare the finite difference equation set necessary to solve the linear boundary value problem with n=5:...
Prepare the finite difference equation set necessary to solve the linear boundary value problem with n=5: y'' + y' + y = x^2, x ∈ [5,10], x(5) = 0, x(10) = 1
Given: The following boundary value problem:    y"+ lamda*y = 0;                0 < x...
Given: The following boundary value problem:    y"+ lamda*y = 0;                0 < x < 2;         y(0) = 0;          y’(2) = 0 Find corresponding eigenvalues, (lamda)n and normalized eigenfunctions yn Expand the function f(x) = x, in terms of the eigen functions obtained in (i)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT