Practice First-order Linear Differential Equations (1.3)

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8 questions

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6 sample questions

Question 1.
What is the general form of a first-order linear differential equation?
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Look for the highest derivative.
Question 2.
What does the variable P(x) represent in this equation?
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Think about how y is influenced.
3Question 3.
What is a first-order linear differential equation?
- dy/dx + P(y) = Q(x)
- dy/dx + P(x)y = Q(x)
- d^2y/dx^2 + P(x)y = Q(x)
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Look for the derivative order.
4Question 4.
The integrating factor µ(x) is defined as e^(∫P(x)dx). Is this statement True or False?
- True
- False
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What is the purpose of the integrating factor again?
Question 5.
Given dy/dx + 4y = sin(x), find y.
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Use the integrating factor, then go to the integration step.
Question 6.
Explain how the solution changes if Q(x) is non-linear. Provide an example.
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Consider the nature of the equation based on Q(x).

4 more questions in this section. Enroll free to practise them all.