(1 pt) if y=e5t is a solution to the differential equationd2ydt2−11dydt+ky=0,find the value of the constant k and the general solution to this equation. k= y= (use constants a, b, etc., for any constants in your solution formula.)

Step-by-step explanation:

given,

and equation

y" - 11 y' + k y = 0...............(1)

now,

Putting value in equation (1)

k = 30

now, differential equation becomes

y" - 11 y' +30 y = 0

( D² - 11 D + 30) y = 0

writing Auxiliary equation'

m² - 11 m + 30 = 0

(m - 5)(m-6) = 0

m = 5,6

now,

a

step-by-step explanation: