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3 years ago

11

If y=e3t is a solution to the differential equation

1 answer:

Zepler [3.9K]3 years ago

4 0

Answer:

k=18, general solution does not exist.

Step-by-step explanation:

If f(t)=y=e3t is a solution to the differential equation

d2ydt2−9dydt+ky=0,

then

y = e^(3t)

y' = dy/dt = 3y

y'' = d2ydt2 = 9y

y'' - 9y' + ky = 0

9y - 9(3y) + ky = 0

(9-27+k)y = 0

solve for y

(9-27+k) = 0

k = 18

general solution is when y=e^(3t)=0, or t-> -infinity

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Read more about linear functions at:

brainly.com/question/15602982

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