Determine whether the function is a solution of the differential equation

y''' - 8y = 0

(a) y = cos(2x)

(b) y = e^(2x)

What exactly is one suppose to do here? Is this suppose to be the third degree because we only covered first degree DE?

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- Jan 31st 2010, 04:34 PMxterminal01Determine whether the function is a solution of the DE?
Determine whether the function is a solution of the differential equation

y''' - 8y = 0

(a) y = cos(2x)

(b) y = e^(2x)

What exactly is one suppose to do here? Is this suppose to be the third degree because we only covered first degree DE? - Jan 31st 2010, 04:36 PMpickslides
Find for each possibility and sub them back into the equation to check.

Sound good? - Jan 31st 2010, 04:37 PMlvleph
Well, you could differentiate the given functions and see if they satisfy the equation, i.e., you want to know if .

- Jan 31st 2010, 04:52 PMxterminal01
- Jan 31st 2010, 04:53 PMlvleph
Your derivative is not correct. .

- Jan 31st 2010, 04:59 PMxterminal01
- Jan 31st 2010, 05:02 PMlvleph
means the third derivative. You are suppose to use the solutions in a) and b) and plug them in the original DEQ. If from a) or b) satisfies then it is a solution to the DEQ.

From a)

and so

So, a) is a solution to the DEQ. Now, check if b) works.