
Differential Equations and Integrating Factors

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

Lucas Foster
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in solving a linear first order differential equation using an integrating factor?
Identify the integrating factor.
Integrate both sides of the equation.
Ensure the equation is in the correct form.
Multiply both sides by the integrating factor.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the equation dy/dt + 3y = t * e^(5t), what is the value of p(t)?
5
e^(5t)
3
t
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the integrating factor μ(t) determined?
By integrating p(t) and raising e to that power.
By setting p(t) equal to zero.
By differentiating p(t).
By multiplying p(t) by y.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the purpose of multiplying the differential equation by the integrating factor?
To find the value of y directly.
To change the variable of integration.
To transform the equation into a simpler form.
To eliminate the constant of integration.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What mathematical rule is applied to verify the transformation of the equation into a derivative form?
Product rule
Power rule
Quotient rule
Chain rule
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the next step after transforming the equation into a derivative form?
Solve for the constant of integration.
Differentiate both sides.
Multiply by another integrating factor.
Integrate both sides.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which integration technique is used to solve the integral of t * e^(8t)?
Direct integration
Trigonometric substitution
Integration by parts
Partial fraction decomposition
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