# Quiz Chapter 10.01: Introduction to Partial Differential Equations

 MULTIPLE CHOICE TEST INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS PARTIAL DIFFERENTIAL EQUATIONS

1. A partial differential equation requires

2. Using substitution, which of the following equations are solutions to the partial differential equation:

• $\dfrac{\partial^{2}u}{\partial x^{2}} = 9 \dfrac{\partial^{2}u}{\partial y^{2}}$

3. The partial differential equation:

• $5 \dfrac{\partial^{2} z}{\partial x^{2}} + 6 \dfrac{\partial^{2} z}{\partial y^{2}} = xy$

is classified as

4. The partial differential equation

• $xy \dfrac{\partial z}{\partial x} = 5 \dfrac{\partial^{2} z}{\partial y^{2}}$

is classfied as

5. The partial differential equation

• $\dfrac{\partial^{2} z}{\partial x^{2}} - 5 \dfrac{\partial^{2} z}{\partial y^{2}} = 0$

is classified as

6. The following is true for the following partial differential equation used in nonlinear mechanics know as the Korteweg-de Vries equation

• $\dfrac{\partial w}{\partial t} + \dfrac{\partial^{3} w}{\partial x^{3}} - 6w \dfrac{\partial w}{\partial x} = 0$