Practice General Form (1.3.1) - Linear Differential Equations - Mathematics (Civil Engineering -1)

Practice: General Form

Lesson 1.3.1Linear Differential Equations

Practise this section

8 questions

Flashcard drill
2 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
2 questions · about 1 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
Define a first-order linear differential equation.
Show hintHide hint
Focus on the terms that make it first-order and linear.
Question 2.
What is a non-homogeneous term?
Show hintHide hint
Consider what additional factors affect the system.
3Question 3.
What form does a first-order linear differential equation take?
- \$ \\frac{dy}{dx} + P(y)x = Q(x) \$
- \$ \\frac{dy}{dx} + P(x)y = Q(x) \$
- \$ dy + P(x)y = Q(y) \$
Show hintHide hint
Remember the relationship between the dependent variable and its rate of change.
4Question 4.
True or False: $Q(x)$ represents the homogeneous part of the equation.
- True
- False
Show hintHide hint
Think about what distinguishes non-homogeneous from homogeneous.
Question 5.
Given a real-world scenario, model it using a first-order linear differential equation. Then, outline the steps you would take to solve it using the integrating factor.
Show hintHide hint
Identify the rate of change and the influences acting on your system.
Question 6.
Create a physical scenario where the rate of a process varies due to external conditions, and derive the associated differential equation.
Show hintHide hint
Consider how environmental factors might alter expected outcomes.

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