Practice Second-order Linear Pdes (3) - Partial Differential Equations

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9 questions

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3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Write the general form of a second-order linear PDE.
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Recall how partial derivatives appear in PDEs.
Question 2.
What is the condition for a PDE to be classified as elliptic?
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Think about the roots of the characteristic equation.
3Question 3.
What classification does the PDE fall under if B² - 4AC > 0?
- Elliptic
- Parabolic
- Hyperbolic
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Think of the wave equation as an example.
4Question 4.
True or False: The Complementary Function is the particular solution to a second-order linear PDE.
- True
- False
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Recall the definitions of CF and PI.
Question 5.
Consider the PDE: 4∂²u/∂x² + ∂²u/∂y² = 0. Classify it based on B² - 4AC and briefly explain your reasoning.
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Identify values of A, B, and C carefully before calculating.
Question 6.
Given the equation: ∂²u/∂x² - ∂²u/∂t² = 0, find the CF by determining the characteristic equation.
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Use the roots to construct the general solution.

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