# Partial Differential Equations : Linear & Quasi-Linear PDEs

## Example Questions

### Example Question #1 : First Order Pd Es

Determine if the statement is true or false:

If the -axis is the axis of symmetry and a surface is revolving around it and  is an arbitrary function, then the partial differential equation associated with that said surface, satisfies the equation:

True

False

True

Explanation:

To determine the truth of this statement, assume the following.

is some function

From here, differential  with respect to  and .

Next eliminate  as it is an arbitrary function.

This leads to the result,

Therefore, the statement,

If the -axis is the axis of symmetry and a surface is revolving around it and  is an arbitrary function, then the partial differential equation associated with that said surface, satisfies the equation:

is true.