5. Differential Equations

Laplace Transforms — Quiz

Test your understanding of laplace transforms with 5 practice questions.

Practice Questions

Question 1

Which of the following is the correct Laplace transform of $f(t) = t^n e^{at}$?

Question 2

When solving a linear ODE with a piecewise forcing function using Laplace transforms, which property or theorem is most commonly applied to handle the time-shifting of the function?

Question 3

Given the differential equation $y''(t) + 2y'(t) + y(t) = 0$ with initial conditions $y(0) = 1$ and $y'(0) = -1$. What is the Laplace transform of the left-hand side of the equation, $L\{y''(t) + 2y'(t) + y(t)\} $?

Question 4

To solve for $Y(s)$ in the s-domain after taking the Laplace transform of an ODE, which algebraic technique is often necessary to prepare the expression for inverse Laplace transformation?

Question 5

What is the inverse Laplace transform of $F(s) = \frac{1}{s^2 + 4s + 5}$?