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mr_godi [17]
3 years ago
15

Solve nonhomogenous equation: x"+4x=cost

Mathematics
1 answer:
motikmotik3 years ago
6 0

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}

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