
Eigenvalues and Boundary Value Problems

Interactive Video
•
Mathematics, Physics
•
11th Grade - University
•
Hard

Amelia Wright
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a boundary value problem?
A problem with infinite solutions.
A problem with no specified solution points.
A problem where the solution is specified at two different points.
A problem where the solution is specified at a single point.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the general solution of a differential equation with complex roots involve?
Logarithmic functions
Polynomial functions
Trigonometric functions
Exponential functions
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the first example, what form does the general solution take?
x = a ln(t) + b
x = a e^t + b e^-t
x = a cos(t) + b sin(t)
x = a t^2 + b t
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why does the first example have infinitely many solutions?
Because the differential equation is not homogeneous.
Because the boundary conditions are not satisfied.
Because the boundary conditions do not provide additional information.
Because the general solution has no arbitrary constants.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the second example, what forces the solution to be unique?
The differential equation is non-homogeneous.
The boundary conditions provide additional information.
The characteristic equation has real roots.
The general solution has no arbitrary constants.
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the characteristic equation for the second example?
r^2 - 2 = 0
r^2 + 2 = 0
r^2 + 1 = 0
r^2 - 1 = 0
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the significance of finding non-zero solutions in boundary value problems?
It indicates the problem is unsolvable.
It helps in determining the uniqueness of solutions.
It is analogous to finding eigenvalues and eigenvectors.
It shows the problem has no boundary conditions.
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