
Understanding Linear First Order Equations and Integrating Factors

Interactive Video
•
Mathematics
•
9th - 10th Grade
•
Hard
Nancy Jackson
FREE Resource
10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the normal form of a linear first order equation?
y' + p(x)y = q(x)
y'' + p(x)y = q(x)
y' = p(x) + q(x)y
y = p(x)y' + q(x)
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In a linear first order equation, what can p(x) and q(x) be?
Functions of both x and y
Only constants
Functions of y
Functions of x or constants
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the purpose of using an integrating factor in solving linear first order equations?
To make the equation non-linear
To find the derivative of y
To eliminate the y term
To convert the equation into a product rule
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the integrating factor for a linear first order equation determined?
e to the power of y
e to the integral of p dx
e to the integral of q dx
ln of the integral of p dx
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the example y' + y = e^x, what is the integrating factor?
x
1
e^(2x)
e^x
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the solution to the equation y' + y = e^x after applying the integrating factor?
y = e^x + C
y = 0.5e^x + Ce^(-x)
y = e^(2x) + C
y = x + Ce^x
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the equation x^2y' + 5xy = x, what is the first step to solve it using the integrating factor method?
Divide by x^2
Multiply by x^2
Add 5xy to both sides
Subtract x from both sides
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