Consider the non-homogeneous system: X' = AX + If the two linearly independent solutions of the associated homogeneous system (X' = AX) are: *-(}) -(':"') then the general solution of the non-homogeneous system is: (in all choices, c1 and c2 are arbitrary constants) C1+C2(1+t)+ e' C1+ C2t C1 +e'+ c2(1+t) + t e' C1+ e'+t e' C1+2e'+2t e' + c3(1 +t) X = C1 + e' + czt - 2t e'

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Consider the non-homogeneous system:
X' = AX +
If the two linearly independent solutions of the associated homogeneous system (X' = AX) are:
X1
X2
then the general solution of the non-homogeneous system is:
(in all choices, c1 and c2 are arbitrary constants)
C1+C2(1+t)+ e'
C1+ Czt
C1+ e'+ c>(1+t) + t e'
C1+e'+t e'
C1+2e'+2t e' + c2(1 + t)
C1+e'+czt - 2t e'
X=
(ai+2e'+c>(1+t) ).
Transcribed Image Text:Consider the non-homogeneous system: X' = AX + If the two linearly independent solutions of the associated homogeneous system (X' = AX) are: X1 X2 then the general solution of the non-homogeneous system is: (in all choices, c1 and c2 are arbitrary constants) C1+C2(1+t)+ e' C1+ Czt C1+ e'+ c>(1+t) + t e' C1+e'+t e' C1+2e'+2t e' + c2(1 + t) C1+e'+czt - 2t e' X= (ai+2e'+c>(1+t) ).
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