Practice General Form (1.5.1) - Linear Differential Equations

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6 sample questions

Question 1.
Write down the general form of a second-order homogeneous linear differential equation.
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Remember, it involves constants and derivatives.
Question 2.
What is the purpose of the auxiliary equation?
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Think of how you find solutions.
3Question 3.
What is the general form of a second-order linear differential equation?
- a²y'' + by' + cy = 0
- y'' + by' + c = 0
- y'' + by = 0
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Look for an equation involving both y and its derivatives.
4Question 4.
True or False: An auxiliary equation is used to find the roots of a given differential equation.
- True
- False
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Consider what role it plays in the problem-solving process.
Question 5.
Determine the general solution for the differential equation: d²y/dx² - 4y = 0.
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Factor the auxiliary equation to find the roots.
Question 6.
How would you solve d²y/dx² + 3dy/dx + 2y = 0?
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Use the quadratic formula or factoring.

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