Properties of hyperbolic functions are given below:
coshnx=(e^n^x+e^-^n^x)/2
sinhnx=e^(nx)-e^(-nx)/2
i) Use idea of elimination to solve for e^nx in terms of coshnx and sinhnx.
ii) Use idea of elimination to solve for e^-nx in terms of coshnx and sinhnx.
iii) Solve equation y''-n^2y=0 as you normally would with auxiliary equation.
iv) Write answer for part (3) using expressions for e^nx and e^-nx from parts (i) and (ii).