Question

Solve nonhomogenous equation: x"+4x=cost

Answer 1

Answer:

$x(t) = Acos 2t + B sin 2t+\frac{cost}{3}$

Step-by-step explanation:

Given is a non homogeneous second degree equation as

$x"+4x=cost$

Auxialary equation is

$m^2+4 =0\\m = 2i, -2i$

Hence general solution is

x = Acos 2t + B sin 2t

Particular integral is = $\frac{cost}{D^2+4}$

Since t has coefficient 1, we substitute

$D^2 =-1\\PI = \frac{cost}{-1+4} =\frac{cost}{3}$

Hence full solution is

$x(t) = Acos 2t + B sin 2t+\frac{cost}{3}$