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## Main Question or Discussion Point

Hiya, I'm having trouble understanding particular integrals at the moment. From what I understand, you have to try trial solutions, unfortunately I've got no idea how to start? Google doesn't turn up anything .. I think I need to examine the equation, and somehow determine its form?

For example this is what i'm currently trying to solve :

Y" + 2y` +2y = cos x

y=?

From my notes, if f(x) = A cos wx + A1 sin wx then y = a0 cos wx + a1 sin wx

From this, I'm guessing A1=0? so y=a1 sin wx

and y' is a1 w cos wx

and y'' is -a1 w^2 wx

And then I'm stuck, how do I now find the PI?

ps. Does anyone have any good notes on the PI and relavent methods to determine what form its in?

Sorry for the messy post, the working came to me as I was typing out the post!

Thanks in advance!

For example this is what i'm currently trying to solve :

Y" + 2y` +2y = cos x

y=?

From my notes, if f(x) = A cos wx + A1 sin wx then y = a0 cos wx + a1 sin wx

From this, I'm guessing A1=0? so y=a1 sin wx

and y' is a1 w cos wx

and y'' is -a1 w^2 wx

And then I'm stuck, how do I now find the PI?

ps. Does anyone have any good notes on the PI and relavent methods to determine what form its in?

Sorry for the messy post, the working came to me as I was typing out the post!

Thanks in advance!