Thread: 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 I need to get it in terms of sinh and cosh. Thanks

You may want to substitute:

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