Finding solutions to equations of motion

[Ed Quanta]

Ok, so I am dealing with a critically damped oscillator in which the natural frequency(w) of the oscillator is equal to the coefficient of friction (y). I am given the force mfe^t and told to find a solution for x, where

x'' +2yx' +w^2 =fe^t.

How do I go about doing this? The solution that I am supposed to find is Afe^t where A=f/4

I have to solve this for f=mfe^-t also, if this requires a different strategy, let me know I guess.

[HallsofIvy]

It would help a lot if you would clarify what you are saying. There is clearly a typo in your equation: it should be
x'' +2yx' +w^2x =fe^t.

But the main problem is that you seem to be using "f" to mean at least two different things. You say "I am supposed to find is Afe^t where A=f/4". Is that f²e^t? But then "I have to solve this for f=mfe^-t". Surely f doesn't mean the same thing on both sides of that equation (since me^-t is not 0!).

[himanshu121]

I doubt whether the Pro is correct

And what are the dimensions on both sides of the solution