Purchase Solution

# Eigenvalues, Eigenfunctions and Differential Equations

Not what you're looking for?

Consider the equation: y'' + k*y = 0 with BC: y(0) = 0 , y(&#61552;) = a &#61625;0

1. What are the restrictions on k such that there is a nontrivial solution?
2. Find a solution using eigenfunction expansion on [0,&#61552;]
3. Find a solution to the differential equation using any method
4. Compare answers 2 and 3 show they are equivalent

See attached file for full problem description.

##### Solution Summary

Eigenvalues, Eigenfunctions and Differential Equations are investigated.

##### Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.

Consider the equation: y'' + k*y = 0 with BC: y(0) = 0 , y() = a 0

1. What are the restrictions on k such that there is a nontrivial solution?

(1) k < 0. Let's write , where . Then the equation becomes and its general solution is . If we use the first boundary condition, y(0) = 0, we get . If we use the second condition y() = a, ...

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.