
Understanding Homogeneous Differential Equations

Interactive Video
•
Mathematics
•
10th - 12th Grade
•
Hard
Standards-aligned

Amelia Wright
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the primary focus of the video series on homogeneous differential equations?
To explore numerical methods for differential equations
To learn about second-order differential equations
To determine if a differential equation is homogeneous
To solve complex differential equations
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
According to the alternative definition, when is a differential equation considered homogeneous?
When F(x, y) is a linear function
When F(TX, TY) equals F(x, y)
When F(x, y) is a quadratic function
When F(x, y) is a constant
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the example provided, what transformation is applied to determine if the equation is homogeneous?
Replace x with y and y with x
Replace x with TX and y with TY
Replace x with TY and y with TX
Replace x with T and y with T
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the purpose of simplifying the expression in the example?
To show that F(TX, TY) equals the original function F(x, y)
To find the roots of the equation
To convert the equation into a linear form
To eliminate the variable T
Tags
CCSS.HSA.APR.D.6
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What common factor is factored out from the denominator in the simplification process?
e^(x/y)
x^2
y^2
t^2
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of simplifying t^2 over t^2 in the example?
t
0
1
t^4
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the significance of the simplification showing F(TX, TY) equals F(x, y)?
It confirms the equation is homogeneous
It indicates the equation is non-homogeneous
It proves the equation is linear
It shows the equation is quadratic
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