1.) (D^2+1)=cosx

2.) y"-3y'-4y=16x-50cos2x

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- Aug 2nd 2007, 09:59 PMalderonnon-homogeneous equation
1.) (D^2+1)=cosx

2.) y"-3y'-4y=16x-50cos2x - Aug 3rd 2007, 12:28 AMCaptainBlack
The general solutions to these take the form of the general solution to the corresponding homogeneous equation plus a particular integral of the non homogeneous equation.

I will presume that you know how to solve the homogeneous equations (which is what I presume your first equation id supposed to be) and

For the first, as is a solution of the homogeneous equation we try a trial solution

For the second we try a trial solution of the form

RonL