8. For what value of k, if any, will y=ke?' +4cos(3x)be a solution to the differential equation y"+9y = 26e 22

(A) 2

(B)

13

5

(C) 26

(D) There is no such value of k.

k = 2

Step-by-step explanation:

As given,

the differential equation is - y'' + 9y = 26      .......(1)

Let the solution of the differential equation be y =

The auxiliary equation becomes

m² + 9 = 0

⇒m² = -9

⇒m = ±√-9

⇒m = ± 3i

So, the complimentary solution becomes

= A cos(3x) + B sin(3x)

Now,

Let the particular solution be = A

⇒ = -2A

and = 4A

Now,

equation (1) becomes

4A + 9 ( A )= 26

⇒4A + 9A  = 26

⇒13A  = 26

By comparing , we get

13A = 26

⇒A = = 2

∴ we get

= 2

so, the solution becomes

y = A cos(3x) + B sin(3x) + 2

As given , the solution y=k +4cos(3x)

So , by comparing with the solution , we get k = 2

So, the correct option is (A) 2.

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!