Covered today: We finished up the material from the handout, concluding with the theorem about the general solution to a non-homogeneous constant coefficient equation.

For next time: page 647 of the handout has some problems. Also, try the following:

1.

Find the general real-valued solution of

y'' + 3y' - 10y = 5

(hint: look for a particular solution which is a constant function)

2.

Find the general real-valued solution of

y'' + 3y' - 10y = 5x

(hint: look for a particular solution which is a linear function)

3.

Find the general real-valued solution of

$$y'' + 3y' - 10y = 5\sin x$$

(hint: look for a particular solution of the form $y_p = A\sin x + B\cos x$)

4.

Find the general real-valued solution of

y'' + y' + y = e^x