4.1. Formation of First-Order PDEs

Try these first

1. 1.

   Define what a first-order PDE is.

   Hint

   Think about the highest order of derivatives involved.

2. 2.

   What is the general form of a first-order PDE?

   Hint

   Recall the notation featured in the section.

3. 3.

   What is the highest order of derivatives in a first-order PDE?

   • 1
   • 2
   • 3

   Hint

   Think about the classification by order.

4. 4.

   True or False: The general form of a first-order PDE is given by F(x, y, z, p, q) = 0.

   • True
   • False

   Hint

   Look back at the general structure discussed.

5. 5.

   Given the function z = 3xy + 2x^2 + c, derive and state the corresponding first-order PDE.

   Hint

   Apply differentiation and focus on the terms needing elimination.

6. 6.

   For the PDE p^2 + q^2 = 1, apply Charpit's method to describe how you would find the complete solution.

   Hint

   Recall the formulations presented in the section for sequential solving.