- #1
bobey
- 29
- 0
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?
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?
