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I think there is something wrong with the question as appears to just have one half of the differential equation and has " and ' - not sure if that should be something else. y-5y+6y=x would mean y-11y=x = -10y=x but as you have nothing it equals to it doesn't really help
Na dude, it's a differential equation, means you have to find such a function y=y(x) which satisfies it. y' and y'' are its derivatives.
according to middle east technical unuversity 's book particular solution is y = x/6 +5/36 :S
but i didnt understand how he find this solution
ah ok - http://www.wolframalpha.com/input/?i=y%27%27-5y%27+%2B6y+%3D+x - wolframalpha pretty useful for helping with equations
factor it as much as you can and do partial fractions on it, the inverse laplace transform
part of your solution will be the solution to the complimentary equation the other part will be the solution to the response of the system due to the forcing function