first of all your second derivative is wrong. The correct expression is:
so after substituting into the differential equation we get:
HINT: has only 2 derivatives before it vanishes. and x has only one....
Use Leibniz's formula to establish that:
is a solution of the differential equation
I know that Leibniz's formula gives the nth derivative of a product of functions, but in this case isn't a product.
So far I've got:
but I'm at a loss as to how to generalise to n.
Help would be hugely appreciated.