Use the method of "undetermined coefficients" to find a particular solution of the differential equation. (The solution found may not include any term that solves the corresponding homogeneous problem.)

y''(x) − 10y'(x) + 61y(x) = −3796 cos(5x) + 185e6x

The particular solution of the differential equation

=  +  

Step-by-step explanation:

Given differential equation y''(x) − 10y'(x) + 61y(x) = −3796 cos(5x) + 185e6x

The differential operator form

Rules for finding particular integral in some special cases:-

      the particular integral ≠ 0

      the particular integral  f(-a^2) ≠ 0

Given problem

Particular integral:-

P.I   =

we will apply above two conditions, we get

=

 on simplification we get

=

=

=

=

 Now particular solution

P.I   =

P.I  =    +  

ad = ae + ed = y + 7

similar triangles therefor

ac/ab = ad/ae

6/4 = (y + 7) / y

cross multiply

6y = 4(y + 7)

6y = 4y + 28

2y = 28

y = 14

step-by-step explanation:

b) well because you get well