
First Order ODEs and Solutions

Interactive Video
•
Mathematics
•
11th Grade - University
•
Hard
Standards-aligned

Sophia Harris
FREE Resource
Standards-aligned
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the form of a first order system of ODEs in vector notation?
X' = P(t) - x(t) * F(t)
X' = P(t) * x(t) + F(t)
X = P(t) * x(t) - F(t)
X' = P(t) + x(t) * F(t)
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is a system of ODEs considered homogeneous?
Because F(t) is a zero vector
Because X(t) is a zero vector
Because P(t) is a zero matrix
Because X' is a zero vector
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the superposition theorem state about solutions of a homogeneous system?
Solutions must be multiplied by zero to remain solutions
Only the product of solutions is a solution
Any linear combination of solutions is also a solution
Only the sum of solutions is a solution
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the Wronskian used for in the context of differential equations?
To solve a system of equations
To calculate eigenvalues
To find the determinant of a matrix
To determine the linear independence of solutions
Tags
CCSS.8.EE.C.7A
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the Wronskian defined in this context?
As the sum of the solutions
As the product of the solutions
As the determinant of a matrix formed by solutions
As the inverse of the solution matrix
Tags
CCSS.8.EE.C.7A
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the example, what indicates that the vector-valued functions are linearly dependent?
The product of two functions equals the third
The sum of two functions equals the third
All functions are zero
The functions are identical
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What change makes the vector-valued functions linearly independent in the example?
Changing all functions to zero
Changing X1 to a constant
Changing X2 to 0t
Changing X3 to a constant
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