4. Partial Differential Equations

Try these first

1. 1.

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

   Hint

   It involves the function and its partial derivatives.

2. 2.

   Define a Complete Integral.

   Hint

   Think about the number of variables involved.

3. 3.

   Which of the following best describes a Partial Differential Equation?

   • An equation involving only one variable.
   • An equation involving derivatives with respect to multiple variables.
   • An equation with no derivatives.

   Hint

   Think about how many variables are involved!

4. 4.

   Lagrange’s method is used primarily for which type of PDEs?

   • True
   • False

   Hint

   Recall the section where we discussed Lagrange's method.

5. 5.

   Given the PDE pz + q sin(y) = cos(x), apply Lagrange's method to find the general solution.

   Hint

   Focus on those auxiliary equations to find independent solutions.

6. 6.

   For the PDE p^2 + qz = 2x apply Charpit's method and derive the complete solution in terms of x, y, and z.

   Hint

   Remember to utilize the nonlinear structure to set your ratios.