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2. Given Y = cje^itx1 + cze^ztx2 + ...+ Cnedntxn is the solution to the initial value problem Y' = AY, Y(0) = Y0. (a) Show that Yo = c1X1+ c2X2• ··+ CnXn. (b) Let X = (x1 X2 C2 Xn) and c = ... Cn Given that the vectors x1, x2, ..., Xn are linearly independent, show that c= X-lYo.

2. Given Y = cje^itx1 + cze^ztx2 + ...+ Cnedntxn is the solution to the initial value problem Y' = AY, Y(0) = Y0. (a) Show that Yo = c1X1+ c2X2• ··+ CnXn. (b) Let X = (x1 X2 C2 Xn) and c = ... Cn Given that the vectors x1, x2, ..., Xn are linearly independent, show that c= X-lYo.

Advanced Engineering Mathematics
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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2. Given Y = cje^itx1 + cze^ztx2 + ...+ Cnedntxn is the solution to the initial value problem Y' = AY, Y(0) = Y0. (a) Show that Yo = c1X1+ c2X2• ··+ CnXn. (b) Let X = (x1 X2 C2 Xn) and c = ... Cn Given that the vectors x1, x2, ..., Xn are linearly independent, show that c= X-lYo.
Transcribed Image Text:2. Given Y = cje^itx1 + cze^ztx2 + ...+ Cnedntxn is the solution to the initial value problem Y' = AY, Y(0) = Y0. (a) Show that Yo = c1X1+ c2X2• ··+ CnXn. (b) Let X = (x1 X2 C2 Xn) and c = ... Cn Given that the vectors x1, x2, ..., Xn are linearly independent, show that c= X-lYo.
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