16.3. Formation of Partial Differential Equations

Try these first

1. 1.

   Differentiate the equation z = 2x + 3y + c with respect to x.

   Hint

   Focus on how differentiating with respect to x only affects terms with x.

2. 2.

   Given z = kx + my + b, identify the method to remove arbitrary constants.

   Hint

   Remember to differentiate the entire equation.

3. 3.

   What do we eliminate to form a PDE from a relation with arbitrary constants?

   • Variables
   • Constants
   • Functions

   Hint

   Think about what we are changing when we differentiate.

4. 4.

   True or False: Arbitrary functions can also be eliminated when forming PDEs.

   • True
   • False

   Hint

   Recall the definitions of arbitrary functions.

5. 5.

   Given the relation z = a * sin(x) + b * cos(y), differentiate and form a PDE by eliminating constants.

   Hint

   What happens if you set the relationship to zero?

6. 6.

   For z = f(x² + y²) + d*e^(x+y), derive a PDE by eliminating the function f and constant d.

   Hint

   Pay attention to your differentiation steps!