Suppose that and are solution of a second order equation is s. In that case the equation is...
... so that the second order ODE is...
show that y1(x) = e^(2+i)x and y2(x) = e^(2-i)x, i=sqrt(-1) are two linearly independent functions
hence obtain a second order linear differential equation with constant coefficients each that y1(x) and y2(x) are its two fundamental solutions.
my attempt :
for the first part, I use the definition of wroskian = y1y2'-y2y1' and show it not equal to zero... ok
the second part, I don't know how to do it...
how to get the second order differential equation????
is that setting : (r+2+i)(r+2-i) to get the auxillary equation??? is that possible??? can someone show me to solve this problem???