FIND THE GENERAL SOLUTION OF THE LINEAR SYSTEM

x'' = 6x+ 2y,y'' = 3x+ 7y

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- May 5th 2009, 05:10 PMbearej50The Method of EliminationFIND THE GENERAL SOLUTION OF THE LINEAR SYSTEM

*x*'' = 6*x*+ 2*y*,*y*'' = 3*x*+ 7*y* - May 5th 2009, 05:45 PMHallsofIvy
Define u= x' and v= y'. Then the differential equation x"= 6x+ 2y becomes u'= 6x+ 2y and y"= 3x+ 7y becomes v'= 3x+ 7y.

So instead of two second order equations we have four first order equations:

x'= u, y'= v, u'= 6x+ 2y, and v'= 3x+ 7y which we could also write as the single first order matrix equation:

And the first step in that is to find the eigenvalues and eigenvectors of the coefficient matrix. - May 6th 2009, 07:24 AMJester