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dx — ах + bу dt Consider a linear system Please select from the following the correct statement. dy — сх + dy dt There could be 3 linearly independent solutions. cos(t) cos(t) + 2 sin(t) and Y2(t) = ( are solutions, they will span the whole solution space sin(t) – cos(t) (i.e., any other solution is a linear combination of these two). sin(t) - cos(t) + sin(t) 2 cos(t) + 4 sin(t) and Y2(1) = are solutions, they will span the whole sin(t) 3 sin(t) solution space (i.e., any other solution is a linear combination of these two). O If there is one solution escaping to infinity (i.e., Y(t) → o as t → +∞), then all the non-zero solutions must escape to infinity.

dx — ах + bу dt Consider a linear system Please select from the following the correct statement. dy — сх + dy dt There could be 3 linearly independent solutions. cos(t) cos(t) + 2 sin(t) and Y2(t) = ( are solutions, they will span the whole solution space sin(t) – cos(t) (i.e., any other solution is a linear combination of these two). sin(t) - cos(t) + sin(t) 2 cos(t) + 4 sin(t) and Y2(1) = are solutions, they will span the whole sin(t) 3 sin(t) solution space (i.e., any other solution is a linear combination of these two). O If there is one solution escaping to infinity (i.e., Y(t) → o as t → +∞), then all the non-zero solutions must escape to infinity.

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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{ dx — ах + by dt Consider a linear system Please select from the following the correct statement. dy — сх + dy dt There could be 3 linearly independent solutions. cos(t) cos(t) + 2 sin(t) If Y1(1) = *) and Ya(1) = are solutions, they will span the whole solution space sin(t) – cos(t) (i.e., any other solution is a linear combination of these two). sin(t) cos(t) + sin(t) Ý20) = ( 3 sin(1) 2 cos(t) + 4 sin(t) If Y1(1) = ") and Y2(0) = are solutions, they will span the whole sin(t) solution space (i.e., any other solution is a linear combination of these two). If there is one solution escaping to infinity (i.e., Y(t) → ∞ as t → +∞), then all the non-zero solutions must escape to infinity.
Transcribed Image Text:{ dx — ах + by dt Consider a linear system Please select from the following the correct statement. dy — сх + dy dt There could be 3 linearly independent solutions. cos(t) cos(t) + 2 sin(t) If Y1(1) = *) and Ya(1) = are solutions, they will span the whole solution space sin(t) – cos(t) (i.e., any other solution is a linear combination of these two). sin(t) cos(t) + sin(t) Ý20) = ( 3 sin(1) 2 cos(t) + 4 sin(t) If Y1(1) = ") and Y2(0) = are solutions, they will span the whole sin(t) solution space (i.e., any other solution is a linear combination of these two). If there is one solution escaping to infinity (i.e., Y(t) → ∞ as t → +∞), then all the non-zero solutions must escape to infinity.
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