Question

(D^2 +4)y=0 solve the differential equations .​

Answer 1

[D^2 +4]y=0

Auxillary equation

m^2 +4=0

m= 2i and -2i

General equation

Y = c1cos2x +c2 sin2x

Answer 2

Given,

differential equation: $(D^{2} +4) y=0$                (1)

To Find,

solve the given equation (1)

Solution,

the equation given is - $(D^{2} +4) y=0$

change in Auxillary equation

$m^{2} +4=0$

m = 2i and -2i

so the general equation is

Y = C1 cos2x + C2 sin2x

Hence the general equation is Y = C1 cos2x + C2 sin2x