# ODE and Linear Algebra again

• Apr 5th 2009, 11:29 AM
thehollow89
ODE and Linear Algebra again
y'' = *y

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.
• Apr 5th 2009, 03:47 PM
ThePerfectHacker
Quote:

Originally Posted by thehollow89
y'' = *y

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 $\cosh (x+y) = \cosh(x)\cosh(y) + \sinh(x) \sinh(y)$.
3)Once expressed in hyperbolic basis replace $\cosh,\sinh$ by exponentials.