Practice General Form Of Solvable Pdes (10.5) - Solution of PDEs by Direct Integration

Practise this section

9 questions

Flashcard drill
3 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
What is a Partial Differential Equation (PDE)?
Show hintHide hint
Look at the definition we discussed in class.
Question 2.
What does direct integration involve?
Show hintHide hint
Consider how we solve simple equations.
3Question 3.
Which of the following is a first-order PDE format?
- ∂²z/∂y² = g(y)
- ∂z/∂x = h(x)
- ∂³z/∂x³ = f(x)
Show hintHide hint
Focus on the order of derivatives.
4Question 4.
True or False: Arbitrary functions are never included in the solutions of PDEs.
- True
- False
Show hintHide hint
Consider the integration process along with our discussions.
Question 5.
Solve the following system of PDEs: ∂z/∂x = x + y and ∂z/∂y = 2x - y.
Show hintHide hint
Make sure to relate your two derived functions.
Question 6.
Given ∂²z/∂x² + ∂²z/∂y² = 0, solve using direct integration by separating variables.
Show hintHide hint
Recap the role of each variable in isolation when integrating.

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