SYSTEMS OF EQUATIONS
CONSIDER THE COUPLED FIRST ORDER SYSTEM OF
DIFFERENTIATE THE SECOND ONE MORE TIME
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