1.

Classify each of the following differential equations according to the categories described in this chapter (ODE or PDE, linear or nonlinear, etc.):

2.

Repeat Exercise 1 for the following equations:

3.

Repeat Exercise 1 for the following equations:

4.

Repeat Exercise 1 for the following equations:

5.

Determine whether each of the functions below is a solution of the corresponding differential equation in Exercise 1:

6.

Determine whether each of the functions below is a solution of the corresponding differential equation in Exercise 2:

7.

Find a function f( t) so that u( t) = tsin ( t) is a solution of the ODE

Is there only one such function f? Why or why not?

8.

Is there a constant f such that u( t) = e _t is a solution of the ODE

9.

Suppose u is a nonzero solution of a linear, homogeneous differential equation. What is another nonzero solution?

10.

Suppose u is a solution of

and v is a (nonzero) solution of

Explain how to produce infinitely many different solutions of (1.9)

1.

1. First-order, homogeneous, linear, nonconstant-coefficient, scalaODE.

2. Second-order, inhomogeneous, linear, constant-coefficient, scalar PDE.

3. First-order, nonlinear, scalar PDE.

2.

3.

1. Second-order, nonlinear, scalar ODE.

2. First-order, inhomogeneous, linear, constant-coefficient, scalar PDE.

3. Second-order, inhomogeneous, linear, nonconstant-coefficient, scalar PDE.

4.

5.

1. No.

2. Yes.

3. No.

6.

7.

There is only one such f: f( t) = tcos (