Use the annihilator method to determine the form of a particular solution for the given equation. u double prime minus 2 u prime minus 8 equals cosine (5 x )plus 7 Find a differential operator that will annihilate the nonhomogeneity cosine (5 x )plus 7

the particular solution is

Y_{p}= C +D\sin 5t +E\cos 5t + F\exp 4t + G\exp -2t

the differential operator that annihilate the non homogeneous differential equation is

D(D^2+5)

Step-by-step explanation:

hello,

i believe the non homogeneous differential equation is

the homogeneous differential equation of the above is

the differential form of the above equation is

thus the roots are 4 and -2.

thus the solution of the homogenous differential equation is given as

the differential operator of the non homogeneous equation is given as

the differential operator annihilates and the differential operator D annihilates 7

applying to both sides of the differential equation we have;

(D-4)(D+2)(u)=\cos 5x +7

the roots of the characteristic polynomial of the diffrential equation above are

thus the particular solution is

this gives us the particular solution

graph b

step-by-step explanation:

one solution- graph a (clear intercepting point.)

no solution- graph b (they're parallel, there will never be a point of interception.)

infinite solutions- graph c (all points intercept.)

im with everythinglos so yeahhhhh

step-by-step explanation: