Differential Equations

Question 1

What is a differential equation?

Answer 1

An equation that contains a derivative or a differential.

Question 2

What is the order of a differential equation?

Answer 2

The highest order derivative that appears in the equation.

Question 3

What is the separation of variables method?

Answer 3

dy/dx = f (x, y) = u(x) v(y)

Question 4

Outline the steps of the separation of variables.

Answer 4

1. Rearrange the equation so there is one variable on either side of the equal sign.
   u(x)dx = v(y)dy
2. Integrate both sides.
3. If boundary conditions are known use them, if not add a constant of integration (+c).

Question 5

How do you solve a second order differential equation?

Answer 5

Integrate twice.