* G) - G )G) + (;) d dt What is the general solution of inhomogeneous state space equations? Eigenvectors. V, = C) = G,), v. = CH) = () V2 generalized eigenvector. a) x1(t) = C, e¬t + C2 (t + 1) e¬t + 4 x2(t) = C, e¬t + C2te=t + 3 b) x1(t) = C, e¬t + C2 (t – 1) e¬t + 2 x2(t) = C, e¬t + Cz t e¬t + 1 x1(t) = C, e¬t + C2 (t – 1) e¬t – 2 x2(t) = -C, e¬t - C2 t e¬t + 7 %3D d) x1 (t) = C, e¬t + Czte¬t + 7 x2(t) = 2 C, e¬t + C2 (2 t – 1) e-t + 10 x1(t) = C, e¬t + C2 (t + 1) e¬t + 8 x2(t) = -C, e¬t - C2 te¬t – 3 x1 (t) = C, e=t + C2te¬t - 1 x2(t) = 2 C, e¬t + C2 (2 t + 1) e¬t - 6

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Chapter2: Second-order Linear Odes
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d
a G) = G )) + G)
dt
What is the general solution of inhomogeneous state space equations?
Eigenvectors.
) = ), v. = C) = ()
V2 generalized sigenvector.
x1(t) = C, e¬t + C2 (t + 1) e¬t + 4
x2(t) = C, e¬t + C2 t e=t + 3
b)
x1(t) = C, e¬t + C2 (t – 1) e¬t + 2
x2(t) = C, e¬t + C2 t e¬t + 1
x1(t) = C, e¬t + C2 (t – 1) e¬t –- 2
x2(t) = -C e¬t - C2 te¬t + 7
d)
x1(t) = C, e¬t + C2t e¬t + 7
x2(t) = 2 C, e¬t + C2 (2 t – 1) e-t + 10
x1(t) = C, e¬t + C2 (t + 1) e¬t + 8
x2(t) = -C e¬t
Cz t e=t
3
x1 (t) = C, e¬t + C2t e¬t - 1
x2(t) = 2 C, e¬t + C2 (2 t + 1) e¬t - 6
Transcribed Image Text:d a G) = G )) + G) dt What is the general solution of inhomogeneous state space equations? Eigenvectors. ) = ), v. = C) = () V2 generalized sigenvector. x1(t) = C, e¬t + C2 (t + 1) e¬t + 4 x2(t) = C, e¬t + C2 t e=t + 3 b) x1(t) = C, e¬t + C2 (t – 1) e¬t + 2 x2(t) = C, e¬t + C2 t e¬t + 1 x1(t) = C, e¬t + C2 (t – 1) e¬t –- 2 x2(t) = -C e¬t - C2 te¬t + 7 d) x1(t) = C, e¬t + C2t e¬t + 7 x2(t) = 2 C, e¬t + C2 (2 t – 1) e-t + 10 x1(t) = C, e¬t + C2 (t + 1) e¬t + 8 x2(t) = -C e¬t Cz t e=t 3 x1 (t) = C, e¬t + C2t e¬t - 1 x2(t) = 2 C, e¬t + C2 (2 t + 1) e¬t - 6
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