# Thread: Annihilator Method?

1. ## Annihilator Method?

Is there anyone well versed in the annihilator method? I don't think I quite fully understand it, and the given problem that we have is:

Solve the given differential equation using the annihilator method

y" - 3y' - 4y = 5e (raised to the) -t

Note: In this case, you have the provide the general solution of the problem.

Any help is appreciated. Thank you!
--Rachel

2. Originally Posted by tibetan-knight
Is there anyone well versed in the annihilator method? I don't think I quite fully understand it, and the given problem that we have is:

Solve the given differential equation using the annihilator method

y" - 3y' - 4y = 5e (raised to the) -t

Note: In this case, you have the provide the general solution of the problem.
No, I don't- you do!

Write this equation in "operator form" as $\displaystyle D^2y- 3Dy- 4y= 4e^{-t}$ which can then be factored as $\displaystyle (D- 4)(D+ 1)y= 4e^{-t}$
Since the derivative of $e^{-t}$ is $-e^{-t}$ it can be "annihilated" by D+1: $(D+1)(4e^{-t}= 0$. That tells us that $\displaystyle (D+1)[(D-4)(D+1)y= (D+1)(4e^{-t}$ so $\displaystyle (D- 4)(D+1)^2y= 0$. Can you solve that?

The general solution to that will have three unknown constants. One of them will be determined by the fact that y must actually satisfy the original equation.

Any help is appreciated. Thank you!
--Rachel