18.2. Introduction

Try these first

1. 1.

   What is the definition of an Ordinary Differential Equation (ODE)?

   Hint

   Think about how these equations describe changes over time.

2. 2.

   Explain what a Laplace Transform does.

   Hint

   Remember the advantages of using transforms over standard methods.

3. 3.

   What does the Laplace Transform do?

   • Converts algebra to calculus
   • Converts functions into the time domain
   • Converts functions into the s-domain

   Hint

   Think about what transformations allow us to do more easily.

4. 4.

   True or False: Laplace Transforms can only be used for linear ODEs.

   • True
   • False

   Hint

   Remember that not all ODEs fit neatly into 'linear' categories.

5. 5.

   Solve the differential equation d^2y/dt^2 + 3dy/dt + 2y = 0 with specified conditions y(0) = 2 and dy/dt (0) = 3 using Laplace Transforms.

   Hint

   Don't forget to handle both initial conditions carefully during transformation.

6. 6.

   Using the Laplace Transform, determine the current i(t) in an RLC circuit satisfying the equation L(d^2i/dt^2) + R(di/dt) + i/C = V(t), with the step function V(t).

   Hint

   Recognize how each component in the circuit interacts as you develop your transformations.