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Consider the following 2nd order nonhomogeneous linear equation x 00 + 4x 0 + 5x = cos 2t

1. Solve for the fundamental solutions of its associated homogeneous equation.

2. Find a particular solution of the nonhomogeneous equation.

3. Based on your answer to the previous two questions, write down the general solution of the nonhomogeneous equation.

Problem II (15 points) Consider the following 2nd order nonhomogeneous linear equation x + 40 + 5x = cos 2t 1. (6 points) S

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Answer #1

som the let given x non - Homogeneous equation is + 4x + 5x & Coszt – 1 To the find the fundamnental son Associated HomogeneoAlso k (t) = -QA (Cosat). +2B.(-sinet).q. :x(t) = – 4 A cosat - 4B sinat / substitute x (t), 2 (t) & X(t) in ean & we get.in eam (n). substitute A t -8A+B=0 BE SA B88 t 65 A from (2) act) = A cosat + B sinet : (x (t) = o Cosat + & sinat . this is

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