Practice Linear First-order Pdes: Lagrange’s Method (4.3)

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6 sample questions

Question 1.
What is a first-order PDE?
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Think about the order of derivatives.
Question 2.
Write the standard form of a first-order linear PDE.
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Recall P, Q, and R represent the coefficients.
3Question 3.
Which of the following is the correct form of a first-order linear PDE?
- Pz + Qy = R
- P(x,y,z)p + Q(x,y,z)q = R(x,y,z)
- d/dx(P) + d/dy(Q) = R
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Pay attention to the variables involved in the equation.
4Question 4.
True or False: Auxiliary equations for Lagrange’s method come from the solution of the PDE itself.
- True
- False
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Think about how we arrive at the auxiliary equations.
Question 5.
Prove the effectiveness of Lagrange’s method by solving a non-homogeneous first-order linear PDE such as z + 2x = y.
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Start with the ratios from the coefficients.
Question 6.
Explore the limits of Lagrange's method by attempting to apply it to a non-linear PDE and discuss the Schrodinger analogy.
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Focus on the non-linearity aspect when setting up your approach.

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