What is the mean, median, and mode?

Mean = 7.5

Median = 7.5

Mode = 5

Step-by-step explanation:

Please refer to the image attached

1. Mean

Mean = Total Sum / Total Number of Entities

Mean = 225/30

         = 7.5

2. Median

Median is the average of the 15th and 16th Entities

15th Entity = 7

16th Entity = 8

Average = (8+7)/2 = 15/2 = 7.5

3. Mode

The entity which gets repeated for most of the times.

From the table we see that 5 gets repeated for 9 times which is highest frequency . hence Mode = 5

y = e^(2x) cos 3x is a explicit solution of y'' − 4y' + 13y = 0

Step-by-step explanation:

y'' − 4y' + 13y = 0   (1)

Verify that y = e^(2x) cos 3x is a explicit solution. We derive this solution:

y'=2e^(2x) cos 3x-3e^(2x) sin 3x     (2)

y''=4e^(2x) cos 3x - 6e^(2x) sin 3x -6e^(2x) sin 3x -9e^(2x) cos 3x

y''=-5e^(2x) cos 3x - 12e^(2x) sin 3x   (3)

In order to verify, we replace (2) (3) in (1):