(;) x-(; )* 1 2 K1 = X' = (cos2t + C2 cos2t (cos2ty sin2t. X = c (o) e cos2t X = c; () e' + cz () te et -sin2t. -sin2t. sin2t. A Ов (sin2t tet \cos2t cos2t cos2t (sin2t X = c (o)et +e X = c1 -sin2t -sin2t. \cos2t.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Given the correct eigenvalues above and the eigenvectors below, what is the general solution of the system: 

= (;) x-(;)*
1
2
X' =
(cos2t
+ C2
cos2t
(cos2ty
sin2t.
X = c (o) e
cos2t
X = c; () e' + cz () te
et
-sin2t.
-sin2t.
sin2t.
A
Ов
(sin2t
tet
\cos2t
cos2t
cos2t
(sin2t
X = c (o)et +e
X = c1
-sin2t
-sin2t.
\cos2t.
O D
Transcribed Image Text:= (;) x-(;)* 1 2 X' = (cos2t + C2 cos2t (cos2ty sin2t. X = c (o) e cos2t X = c; () e' + cz () te et -sin2t. -sin2t. sin2t. A Ов (sin2t tet \cos2t cos2t cos2t (sin2t X = c (o)et +e X = c1 -sin2t -sin2t. \cos2t. O D
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