Practice Linear PDEs (Lagrange's Method) - 2.1 | Partial Differential Equations | Mathematics III (PDE, Probability & Statistics)
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Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the standard form of a Linear PDE?

πŸ’‘ Hint: Remember the structure involving partial derivatives.

Question 2

Easy

True or False: Lagrange's method can only be used for second-order PDEs.

πŸ’‘ Hint: Think about the order of the derivatives involved.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What are the three components of a Linear PDE in standard form?

  • P(x,y,z)
  • Q(x,y,z)
  • R(x,y,z)
  • All of the above

πŸ’‘ Hint: Recall what components make up the PDE.

Question 2

True or False: Lagrange's method can find solutions for any type of PDE.

  • True
  • False

πŸ’‘ Hint: Consider the applicability of the method.

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Challenge Problems

Push your limits with challenges.

Question 1

Prove that the general solution of the Linear PDE $\frac{\partial z}{\partial x} + \frac{\partial z}{\partial y} = 0$ can be expressed in terms of functions of $u$ and $v$. Find such functions.

πŸ’‘ Hint: Recall the characteristics method using Lagrange's approach.

Question 2

Using Lagrange’s method, solve the following linear PDE: $2xy\frac{\partial z}{\partial x} + 4z\frac{\partial z}{\partial y} = x^2$.

πŸ’‘ Hint: Focus on integrating each term from the auxiliary framework.

Challenge and get performance evaluation