Question

Find the general solution of differential equation (d^2-4d+2)y=0

Answer 1

We have given the differential equation:

$(D^2-4D+2)y = 0$

Its auxiliary equation can be written as :

$m^2-4m+2 = 0$

$m = \dfrac{4 \pm 4i}{2}$

$m = 2 \pm 2i$

Hence, its solution can be written as,

$y = e^{2x}(C_1cos2x+C_2sin2x)$