
Understanding Particular Solutions in Differential Equations

Interactive Video
•
Mathematics
•
11th Grade - University
•
Medium

Lucas Foster
Used 2+ times
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the primary focus when dealing with particular solutions in non-homogeneous differential equations?
Finding the roots of the equation
Checking for repetition of terms
Calculating the derivative
Solving for constants
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the example with distinct real roots, what form does the complementary function take?
C1 * e^(3x) + C2 * e^(-2x)
C1 * e^(x) + C2 * e^(-x)
C1 * e^(2x) + C2 * e^(-3x)
C1 * e^(x) + C2 * e^(2x)
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
When dealing with repeated real roots, what adjustment is made to the particular solution?
Add a constant
Multiply by an exponential
Add an extra factor of the independent variable
Subtract a factor of the independent variable
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the characteristic equation used for in solving differential equations?
To check for repetition
To solve for constants
To determine the complementary function
To find the derivative
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the example with complex roots, what form does the complementary function take?
C1 * cos(x/3) + C2 * sin(x/3)
C1 * e^(x) + C2 * e^(-x)
C1 * e^(3x) + C2 * e^(-3x)
C1 * cos(x) + C2 * sin(x)
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How are complex roots represented in the characteristic equation?
As real numbers
As exponential terms
As imaginary numbers
As alpha plus or minus beta i
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the effect of complex roots on the form of the complementary function?
It remains unchanged
It becomes exponential
It becomes a polynomial
It includes sine and cosine terms
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