Question

Y''-4y=cosx find general solution.

Answer 1

Explanation:

`y''-4y=cosx`

The auxialary equation and solutions are as follows:

`m^2-4=0\\m=2,-2`

General solution is

`y=Ae^(2x) +Be^(-2x)`

Right side =cosx

Particular Integral

=
`(cosx)/(-1-4) =(-cosx)/(5)`

Hence full solution is