6.5. Example Problem

Try these first

1. 1.

   Define a Partial Differential Equation.

   Hint

   Think about functions of more than one variable.

2. 2.

   What is the purpose of Charpit’s Method?

   Hint

   It’s systematic!

3. 3.

   What form must a PDE take for Charpit’s Method?

   • F(x,y,z,p,q)=0
   • F(x,y,z)=0
   • F(p,q)=0

   Hint

   Look for the inclusion of partial derivatives.

4. 4.

   True or False: Charpit's Method can be applied to linear PDEs.

   • True
   • False

   Hint

   Consider the nature of the equations.

5. 5.

   Given the PDE z = p(x^2 + y^2) + q(xy), outline the steps in Charpit's Method to derive its general solution.

   Hint

   Start with standard form and derive each step carefully.

6. 6.

   Explain how the complete integral found from Charpit’s Method can assist in solving initial value problems in higher dimensions.

   Hint

   Think about how generalities help in specific cases.