# Thread: ODE and Linear Algebra

1. ## ODE and Linear Algebra

y'' = +λ^2*y
Show cosh( λt) and sinh( λt) form an alternate basis for our
λ^2– eigenspace.

Any help fellas?

2. Originally Posted by thehollow89
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 $\sinh (\lambda x)$ and $\cosh (\lambda x)$ are linearly independent (here it is assumed that $\lambda > 0$) solutions to the differencial equation. To see that just use the Wronskian.