What particular integral should I use for SODE cosh2x

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thomas49th
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Homework Statement


Hi, I've been asked to find the solution of y'' + 6y' + 8y = 12cosh2x

Homework Equations


The Attempt at a Solution



Well the complmentry function is Ae^-2x + Be^-4x

This creates a problem when trying our PI because we cannot try Ccosh2x and Dsinh2x because the hyperbolic functions contain e^-2x, which appears in our CF. Apparently I should try a PI of Ee^2x + (F+Gx)e^-2x, but I cannot see where on Earth this comes from? Why can't I try Ee^2x + Fxe^-2x. It must be simple :\

Thanks
 
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hi thomas49th! :wink:
thomas49th said:
This creates a problem when trying our PI because we cannot try Ccosh2x and Dsinh2x because the hyperbolic functions contain e^-2x, which appears in our CF. Apparently I should try a PI of Ee^2x + (F+Gx)e^-2x, but I cannot see where on Earth this comes from? Why can't I try Ee^2x + Fxe^-2x. It must be simple :\

yes, i think you're right :smile:

if Ee2x + (F+Gx)e-2x is a PI, then so is Ee2x + Gxe-2x …

any solution is a PI ! :rolleyes: