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

Practice - Second-Order Linear PDEs

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Write the general form of a second-order linear PDE.

💡 Hint: Recall how partial derivatives appear in PDEs.

Question 2 Easy

What is the condition for a PDE to be classified as elliptic?

💡 Hint: Think about the roots of the characteristic equation.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What classification does the PDE fall under if B² - 4AC > 0?

Elliptic
Parabolic
Hyperbolic

💡 Hint: Think of the wave equation as an example.

Question 2

True or False: The Complementary Function is the particular solution to a second-order linear PDE.

True
False

💡 Hint: Recall the definitions of CF and PI.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Consider the PDE: 4∂²u/∂x² + ∂²u/∂y² = 0. Classify it based on B² - 4AC and briefly explain your reasoning.

💡 Hint: Identify values of A, B, and C carefully before calculating.

Challenge 2 Hard

Given the equation: ∂²u/∂x² - ∂²u/∂t² = 0, find the CF by determining the characteristic equation.

💡 Hint: Use the roots to construct the general solution.

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