Answer:
[tex]x(t) = Acos 2t + B sin 2t+\frac{cost}{3}[/tex]
Step-by-step explanation:
Given is a non homogeneous second degree equation as
[tex]x"+4x=cost[/tex]
Auxialary equation is
[tex]m^2+4 =0\\m = 2i, -2i[/tex]
Hence general solution is
x = Acos 2t + B sin 2t
Particular integral is = [tex]\frac{cost}{D^2+4}[/tex]
Since t has coefficient 1, we substitute
[tex]D^2 =-1\\PI = \frac{cost}{-1+4} =\frac{cost}{3}[/tex]
Hence full solution is
[tex]x(t) = Acos 2t + B sin 2t+\frac{cost}{3}[/tex]
