Answer:
Step-by-step explanation:
Let 
, that is a be any real number.
The inverse property of addition says that, the sum of a number 
and its additive inverse 
gives the identity element of addition which is zero.
That is :
We can rewrite this as 
From the above options, we have the correct answer to be the first choice
3 x -2^(n-1)
To answer this question, first solve the equation 3 x -2^(n-1) for n=1, n=2,
n=3, n=4, and n=5.
Where n=1
3 x -2^(1-1)
3 x -2^0
3 x 1
n1 = 3
Where n=2
3 x -2^(2-1)
3 x -2^1
3 x -2
n2 = -6
Where n=3
3 x -2^(3-1)
3 x -2^2
3 x 4
n3 = 12
Where n=4
3 x -2^(4-1)
3 x -2^3
3 x -8
n4 = -24
Where n=5
3 x -2^(5-1)
3 x -2^4
3 x 16
n5 = 48
The next step is to find the summation by adding n1 + n2 + n3 + n4 + n5.
3 + (-6) + (12) + (-24) + (48) =
3 - 6 + 12 - 24 + 48
= 33
The answer is C. 33
We can try reduction order and look for a solution 
. Then
Substituting these into the ODE gives
which leaves us with an ODE linear in 
:
This ODE is separable; divide both sides by the coefficient of 
and separate the variables to get
Integrate both sides; on the right, substitute 
so that 
.
Now solve for 
,
then for 
,
Solve for 
by integrating both sides.
Substitute again and solve for 
:
then for ,
So the second solution would be
already accounts for the second term of the solution above, so we end up with
as the second independent solution.
