# Thread: Higher Order Complex Roots

1. ## Higher Order Complex Roots

Find the general solution of the given differential equation:

$
y^{6} - 3y^{4} + 3y'' - y = 0
$

2. Originally Posted by fudawala
Find the general solution of the given differential equation:

$
y^{6} - 3y^{4} + 3y'' - y = 0
$
$k^6 - 3k^4 + 3k^2 - 1 = 0$

$(k^2-1)^3 = 0$

$(k-1)(k-1)(k-1)(k+1)(k+1)(k+1)=0$

$y=Ae^x+Bxe^x+Cx^2e^x+De^{-x}+Exe^{-x}+Fx^2e^{-x}$