1.1. Introduction

Try these first

1. 1.

   Define a differential equation.

   Hint

   Think about the components of the equation.

2. 2.

   What is the difference between first-order and second-order differential equations?

   Hint

   Consider the number of derivatives present.

3. 3.

   What is a linear differential equation?

   • A polynomial equation
   • An equation where derivatives are not raised to a power higher than one
   • An equation of any degree

   Hint

   Think about the meaning of 'linear' in mathematics.

4. 4.

   True or False: All differential equations are linear.

   • True
   • False

   Hint

   Recall the definition of linearity.

5. 5.

   A civil engineer needs to model the deflection of a beam under varying loads. Construct a first-order linear differential equation representing the load analysis.

   Hint

   Consider how loads change over distance or time.

6. 6.

   Given a second-order linear differential equation for structural vibration, explain how the roots of its auxiliary equation will affect the response of the structure.

   Hint

   Reflect on how oscillations look based on the type of roots.