Verify that cosh( λt - 4) is a solution to our ODE. Express this function in terms of both our old exponential basis, and our new hyperbolic basis.
1)To show this is a solution just substitute.
2)To express in hyperbolic basis use $\displaystyle \cosh (x+y) = \cosh(x)\cosh(y) + \sinh(x) \sinh(y)$.
3)Once expressed in hyperbolic basis replace $\displaystyle \cosh,\sinh$ by exponentials.