Practice Laplace Transforms & Applications (18) - Application to Ordinary Differential Equations (ODEs)

Practice: Laplace Transforms & Applications

Lesson 18Application to Ordinary Differential Equations (ODEs)

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 the definition of a Laplace Transform?
Show hintHide hint
Look for the integral representation.
Question 2.
What are initial conditions, and why are they important in ODEs?
Show hintHide hint
Think about what values you need to begin solving.
3Question 3.
What is the primary purpose of using Laplace Transforms?
- To convert time functions to algebraic equations
- To graph functions
- To derive new functions
Show hintHide hint
Consider what advantage Laplace Transforms provide.
4Question 4.
True or False: Initial conditions can be skipped when using Laplace Transforms.
- True
- False
Show hintHide hint
Think about the role of conditions in solving ODEs.
Question 5.
Given $\frac{d^2y}{dt^2} + 4y = 5$ with initial conditions $y(0) = 1$ and $y'(0) = 0$ , apply Laplace Transforms to solve.
Show hintHide hint
Consider what changes with the presence of initial conditions.
Question 6.
An RLC circuit has $L=2, R=3$ . Write its ODE, apply Laplace Transforms, and find the current function using a step input.
Show hintHide hint
Relate circuit parameters to their roles in the differential equation.

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