1.2.2. Example 4

Try these first

1. 1.

   Define a Partial Differential Equation (PDE).

   Hint

   Think of what 'partial' means in terms of derivatives.

2. 2.

   What are arbitrary constants?

   Hint

   Consider constants in a linear equation.

3. 3.

   What does PDE stand for?

   • Partial Derivative Equations
   • Partial Differential Equations
   • Partially Defined Equations

   Hint

   Remember it relates to derivatives.

4. 4.

   True or False: Arbitrary constants in a PDE can change without affecting the equation's characteristics.

   • True
   • False

   Hint

   Consider constants in mathematical functions.

5. 5.

   Consider the function z = asin(x) + bcos(y) + d. Derive the PDE by eliminating arbitrary constants a, b, and d.

   Hint

   Consider how those derivatives relate to sinusoidal functions.

6. 6.

   Given z = f(x² + y²) + h(x - y), derive the PDE by eliminating arbitrary functions f and h.

   Hint

   What substitutions can simplify the process?