# Math Help - Getting into correct form

1. ## 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

2. ## Re: Getting into correct form

You may want to substitute:

$e^x = \cosh x + \sinh x$
$e^{-x} = \cosh x - \sinh x$

3. ## Re: Getting into correct form

That does the trick. Redefining constants, y=(A+Bx)coshx+(C+Dx)sinhx.