Use the method of variation of parameters to find a particular solution of the given differential equation. Then check your answer by using the method of undetermined coefficients. y'' − 5y' + 6y = 2et

Therefore the complete primitive is

Therefore the general solution is

Step-by-step explanation:

Given Differential equation is

Let be a trial solution.

and

Then the auxiliary equation is

∴The complementary function is

To find P.I

First we show that and are linearly independent solution.

Let  and

The Wronskian of and is

                                                  ≠ 0

∴ and are linearly independent.

Let the particular solution is

Then,

Choose and such that

.......(1)

So that

Now

.......(2)

Solving (1) and (2) we get

   and  

Hence

and  

Therefore

Therefore the complete primitive is

∴The complementary function is

The particular solution is

Then,

and

Therefore the general solution is

the answer for your question is

step-by-step explanation:

p(x)= 8 x³ - 36 x² + 54 x - 27

q(x) = 2 x -3

you can check your mistake and then you can choose the correct option.

dividend =   8 x³ - 36 x² + 54 x - 27

divisor = 2 x -3

if you want to find quotient, proceed as follows

q(x)= 0

2 x - 3=0

x =

now , i have used division method , to find quotient and remainder