y'' = +λ^2*y
Show cosh( λt) and sinh( λt) form an alternate basis for our
λ^2– eigenspace.
Any help fellas?
You just need to show that $\displaystyle \sinh (\lambda x)$ and $\displaystyle \cosh (\lambda x)$ are linearly independent (here it is assumed that $\displaystyle \lambda > 0$) solutions to the differencial equation. To see that just use the Wronskian.