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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Solve the PDE βz/βx = x + 3. What is the function z?
π‘ Hint: Think about integrating with respect to x.
Question 2
Easy
What is an arbitrary function in the context of PDEs?
π‘ Hint: Remember how we treat constants in single variable integration.
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 method do we use to solve PDEs like βz/βx = 2x + y?
- Integration
- Differentiation
- Summation
π‘ Hint: Think about how to find the function from its rate of change.
Question 2
True or False: An arbitrary function of y appears during the integration process in PDEs.
- True
- False
π‘ Hint: Reconsider how constants of integration behave in multi-variable cases.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Solve the PDE βz/βx = 3e^x + sin(y) and indicate the form of the arbitrary function.
π‘ Hint: Pay close attention to the exponential function when integrating.
Question 2
Given the PDEs βz/βx + βz/βy = xy and βz/βy = x-yΒ², use both to find an expression for z.
π‘ Hint: Link the two equations through integration and differentiation to extract solutions.
Challenge and get performance evaluation