How do you use the Method of Undetermined Coefficients when the right side of the equation (x(t)) is not a given function. AKA - y(t) + 5y'(t) = x(t)

Question

anonymous · Answer

You need to take the characteristic equation and set that equal to zero. Once and ONLY once you do that you can solve for the rest of the equation. I also recommend using the LaPLACE method for help.

anonymous · Answer

Isn't the total answer the general solution + the particular solution? So that the general solution is the answer as if it were homogenous, but how do you find the particular solution?

anonymous · Answer

The characteristic equation would be 1+ 5r = 0, r = -1/5.
So I have $$y = ce ^{-1/5t}$$
however wolfram alpha shows the answer as 
$$y = ce ^{-1/5t} + x - 5$$

anonymous · Answer

Did you look at the hints?

anonymous · Answer

Sorry what hints? http://www.wolframalpha.com/input/?i=y+%2B+5y%27+%3D+x