SYSTEMS OF EQUATIONS

CONSIDER THE COUPLED FIRST ORDER SYSTEM OF

LINEAR O.D.E.S

x’ = ax + by

y’ = Ax + By

DIFFERENTIATE THE SECOND ONE MORE TIME

y’’ = Ax’ + By’

Substitute for x’ from the first equation

y’’ = A(ax + by) + By’ = a(Ax) + Aby + By’

Substitute for Ax from the second equation

y’’ = a(y’ - By) + Aby + By’ = (a + B)y’ + (Ab-Ba)y

THUS THE SYSTEM IS SECOND ORDER

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