let us try solving the general case:
consider the operator , then we can transform the equation into , where (i have to change our variable to y because we need the imaginary number ).
but the middle one is also equal to
also using similar arguments, it can be shown that
if we take and , then we have the general solution:
now, to solve for the value of and , just consider that
equate equation 1 to 0.
solve for the first derivative of that equation 1 and equate to 0..
now you have two equations with two unknowns .. can you contnue it?
i'm late for my class...