( a ) Show that the functions x ( t ) = 3 e t + 7 e − t and y ( t ) = 3 e t + 21 e − t are solutions of the system x ' = 2 x − y , y ' = 3 x − 2 y , Satisfying the initial conditions x ( 0 ) = 10 and y ( 0 ) = 24 . ( b ) Use a computer to plot the graphs of x and y versus t .
( a ) Show that the functions x ( t ) = 3 e t + 7 e − t and y ( t ) = 3 e t + 21 e − t are solutions of the system x ' = 2 x − y , y ' = 3 x − 2 y , Satisfying the initial conditions x ( 0 ) = 10 and y ( 0 ) = 24 . ( b ) Use a computer to plot the graphs of x and y versus t .
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