# Getting into correct form

• Dec 23rd 2011, 10:06 AM
Duke
Getting into correct form
I'm part way through a question, just need help at the end.

I found the characteristic equation for a fourth order DE with constant co-efficents (and homogeneous) was r^4 - 2r^2 +1=0 so the roots are r = 1, -1 each with multiplicity 2.

so $y=e^x(A+Bx)+e^{-x}(B+Dx)$ I need to get it in terms of sinh and cosh. Thanks
• Dec 23rd 2011, 10:17 AM
ILikeSerena
Re: Getting into correct form
You may want to substitute:

$e^x = \cosh x + \sinh x$
$e^{-x} = \cosh x - \sinh x$
• Dec 23rd 2011, 10:19 AM
Duke
Re: Getting into correct form
That does the trick. Redefining constants, y=(A+Bx)coshx+(C+Dx)sinhx.