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1. Consider the linear system i1 = -2px1 + qx2 i2 -qx1 – pgx2 where p and q are unspecified parameters. How should p and q be chosen to ensure that the solutions of this system have the form X1(t) + be-2t = ae X2(t) = ce-t + de-2t for any choice of initial conditions? Is your answer unique? Explain.

1. Consider the linear system i1 = -2px1 + qx2 i2 -qx1 – pgx2 where p and q are unspecified parameters. How should p and q be chosen to ensure that the solutions of this system have the form X1(t) + be-2t = ae X2(t) = ce-t + de-2t for any choice of initial conditions? Is your answer unique? Explain.

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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1. Consider the linear system i1 = -2px1 + qx2 i2 -qx1 – pgx2 where p and q are unspecified parameters. How should p and q be chosen to ensure that the solutions of this system have the form X1(t) + be-2t = ae X2(t) = ce-t + de-2t for any choice of initial conditions? Is your answer unique? Explain.
Transcribed Image Text:1. Consider the linear system i1 = -2px1 + qx2 i2 -qx1 – pgx2 where p and q are unspecified parameters. How should p and q be chosen to ensure that the solutions of this system have the form X1(t) + be-2t = ae X2(t) = ce-t + de-2t for any choice of initial conditions? Is your answer unique? Explain.
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