Question

If y=e^2t is a solution of y"-5y'+ky = 0, then the value of k is​

Answer 1

Answer:

y"=4e^2t=4y

y'=2e^2t=2y

#answer is

4y-10y+KY=0

k=6

Answer 2

Given:

y" - 5y' + ky = 0.

y = e^2t.

To Find:

The value of k.

Solution:

Here,

y' = e^2t.dt. = 2e^2t = 2y.

and, y'' = 2e^2t.dt. = 4e^2t = 4y.

Now,

Putting the values of y' and y" in the equation,

y" - 5y' + ky = 0.

4y - 5*2y + ky = 0.

4y - 10y + ky = 0.

-6y + ky = 0.

ky = 6y

So, k = 6.

Hence, the value of k is 6.