# Property of solution of a system of differential equations

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We answer the following question,

The system of differential equations:

u'=v, v'=-u,

A. Does not have any nonzero solution.

B. Has only periodic solutions.

C. Has only unbounded solutions.

D. Has only solutions that decay to zero at infinity.

E. Has some unbounded solutions.

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##### Solution Summary

Given a linear system of two differential equations we answer whether the solutions are periodic, unbounded or with decay at infinity.

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The system of differential equations is:

(1) y_1'=y_2 and

(2) y_2'=-y_1.

Then, differentiating both ...

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