1.1.2. Example 2

Try these first

1. 1.

   Define a Partial Differential Equation.

   Hint

   Think about how these equations relate to functions.

2. 2.

   What is the first step in eliminating arbitrary constants?

   Hint

   Remember, you're looking to find derivatives!

3. 3.

   What does a Partial Differential Equation involve?

   • Only derivatives
   • Partial derivatives of multivariable functions
   • Only functions

   Hint

   Consider what it means to have multiple independent variables.

4. 4.

   True or False: PDEs can represent real-world phenomena.

   • True
   • False

   Hint

   Reflect on the applications of equations.

5. 5.

   Given the equation z = e^(x) + cos(y + a), eliminate the constant a and form the corresponding PDE.

   Hint

   Remember to differentiate each term and substitute intelligently.

6. 6.

   From z = exp(x^2 + y^2), eliminate the function f and express the result as a PDE.

   Hint

   Relate your p and q effectively!