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)

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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)

Mathematics
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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.
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?
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 \[y = ce ^{-1/5t} + x - 5\]

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

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