What particular integral should I use for SODE cosh2x

[thomas49th]

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

 

[tiny-tim]

hi thomas49th!

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

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

any solution is a PI !