10.4 - Examples of Direct Integration
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Practice Questions
Test your understanding with targeted questions
Solve the PDE ∂z/∂x = x + 3. What is the function z?
💡 Hint: Think about integrating with respect to x.
What is an arbitrary function in the context of PDEs?
💡 Hint: Remember how we treat constants in single variable integration.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What method do we use to solve PDEs like ∂z/∂x = 2x + y?
💡 Hint: Think about how to find the function from its rate of change.
True or False: An arbitrary function of y appears during the integration process in PDEs.
💡 Hint: Reconsider how constants of integration behave in multi-variable cases.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Solve the PDE ∂z/∂x = 3e^x + sin(y) and indicate the form of the arbitrary function.
💡 Hint: Pay close attention to the exponential function when integrating.
Given the PDEs ∂z/∂x + ∂z/∂y = xy and ∂z/∂y = x-y², use both to find an expression for z.
💡 Hint: Link the two equations through integration and differentiation to extract solutions.
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