Practice Solution Method: Integrating Factor (if) (1.3.2)

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6 sample questions

Question 1.
What is the form of a first-order linear differential equation?
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Look for the terms dy/dx and the functions of x.
Question 2.
Define an Integrating Factor.
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Think about how it helps in integration.
3Question 3.
What is the purpose of the Integrating Factor in differential equations?
- To multiply the dependent variable
- To simplify the equation for integration
- To find the derivative directly
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Think about what happens when we apply it to the left side of the equation.
4Question 4.
True or False: The Integrating Factor is always e^(∫P(x)dx).
- True
- False
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Recall the formula we discussed for calculating the Integrating Factor.
Question 5.
Solve the differential equation dy/dx + 2y = sin(x).
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Focus on integrating the right side after applying the Integrating Factor.
Question 6.
A tank fills with water at a rate described by dy/dt + 0.5y = 10. Find y(t).
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Use the Integrating Factor and initial conditions to simplify and solve.

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