Practice Lagrange’s Auxiliary Equations - 4.3.2 | 4. First-Order PDEs | Mathematics - iii (Differential Calculus) - Vol 2
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Lagrange’s Auxiliary Equations

4.3.2 - Lagrange’s Auxiliary Equations

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define a first-order PDE in your own words.

💡 Hint: Focus on the term 'first derivative' in your definition.

Question 2 Easy

What are auxiliary equations used for?

💡 Hint: Think about how we relate differentials to one another.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the form of a first-order linear PDE?

F(x
y
z
p
q) = 0
P(x
y
z)p + Q(x
y
z)q = R(x
y
z)
∂z/∂x + ∂z/∂y = 0

💡 Hint: Look for the setup that mentions P, Q, and R.

Question 2

True or False: The auxiliary equations are used to derive two independent solutions.

True
False

💡 Hint: Think about how we apply these equations.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given the PDE pz + 2qy = 3x, set up the auxiliary equations and find the general solution.

💡 Hint: Focus on integrating the ratios correctly.

Challenge 2 Hard

Explain how varying the auxiliary equations impacts the outcome of the general solution.

💡 Hint: Consider the role of different inputs into the same formula.

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Reference links

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