Practice Step-by-step Procedure (10.3) - Solution of PDEs by Direct Integration

Practice: Step-by-Step Procedure

Lesson 10.3Solution of PDEs by Direct Integration

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8 questions

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6 sample questions

Question 1.
Integrate $\frac{\partial z}{\partial x} = 5x$ .
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Remember to treat y as a constant.
Question 2.
What is the result of integrating $\frac{\partial z}{\partial y} = 3y^2$ ?
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Think about what happens to x during this integration.
3Question 3.
What is direct integration used for?
- Solving ordinary differential equations
- Solving Partial Differential Equations
- Finding limits of functions
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Think about which type of equations involve partial derivatives.
4Question 4.
When given $\frac{\partial z}{\partial x} = f(x,y)$ , we integrate with respect to which variable?
- True
- False
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This ensures we correctly find \$ z \$ as a function of both variables.
Question 5.
Given the PDEs $\frac{\partial z}{\partial x} = 3x^2$ and $\frac{\partial z}{\partial y} = 4y$ , derive the function z.
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Remember to add both arbitrary functions after integration.
Question 6.
For the PDE $\frac{\partial z}{\partial x} = sin(xy)$ , integrate to find z where y is treated as constant.
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Recall how we adjust our integration based on treating y as a constant.

4 more questions in this section. Enroll free to practise them all.