Just DO it! With k= 5, those functions are . Find the second derivative, plug it into the equation and see what happens! With k= -5, you haved . Since sinh is an odd function and cosh is an even function, that is just which is really the same thing since A itself can be positive or negative.but I'm struggling with the other two parts of the question:
For those values of , show that every member of the family of functions (where and are constants) is also a solution of the DE.
[/quote]Come up with a second order DE for which is a solution for the same values of obtained before.[/QUOTE]
So now youy are working with . Take the second derivative, stare at it and think!