4.1.1. From a Function

Try these first

1. 1.

   What do you understand by a first-order PDE?

   Hint

   Focus on the highest derivative in the equation.

2. 2.

   Identify the arbitrary constants in the function z = 3x + 2y + 5.

   Hint

   Look for the numbers that can change in the equation.

3. 3.

   What does a first-order PDE involve?

   • Only zero derivatives
   • First derivatives
   • Second derivatives

   Hint

   Think about what 'first-order' implies.

4. 4.

   True or false: Arbitrary constants can be eliminated to form first-order PDEs.

   • True
   • False

   Hint

   Consider the role of constants in the function.

5. 5.

   Given the function z = 5x^2 + 3xy + 7, derive the PDE by eliminating constants.

   Hint

   Remember to differentiate before eliminating.

6. 6.

   Given f(x,y) = 2xy + c, detail how to form a PDE and explain the significance of c.

   Hint

   Consider what happens to the function when c is removed.