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  =    +  

t = 3

step-by-step explanation:

put t = 3 in this expression :

(3²-1)(3²-2)(3² - 3)(3² - 4) = 8×7×6×5 = 56×30 = 1680