[ ( D^2 + 2 ) ^ 2 ] * y = 0, where D=dy/dx ------ (1)
let, y=e^mx be the trial solution of the equation (1), then we get -
[ ( D^2 + 2 ) ^ 2 ] * e^mx = 0
A.E = ( m^2 + 2 ) ^ 2 = 0
=> m^2 + 2 = 0
=> m^2 = -2
=> m^2 = 2( i^2 )
=> m = ± √2i
I'm stuck till here, the question is, what will be the general solution of this?
This? --> y = c1 cos √2x + c2 sin √2x
Or This? --> y = c1 cos √2x + c2x sin √2x
Or Something Else??
let, y=e^mx be the trial solution of the equation (1), then we get -
[ ( D^2 + 2 ) ^ 2 ] * e^mx = 0
A.E = ( m^2 + 2 ) ^ 2 = 0
=> m^2 + 2 = 0
=> m^2 = -2
=> m^2 = 2( i^2 )
=> m = ± √2i
I'm stuck till here, the question is, what will be the general solution of this?
This? --> y = c1 cos √2x + c2 sin √2x
Or This? --> y = c1 cos √2x + c2x sin √2x
Or Something Else??