im trying to solve a system of differential equations of (x''(t ) + 5(x(t )) - 2y(t ) = 0
and, -2*x(t ) + y''(t ) +2*y(t ) = 0
but I keep getting the wrong answer..
Here's an outline of the solution. Write the equations as
or in vector form .
Now diagonalise that matrix . You should find that the eigenvalues are –1 and –6, with corresponding eigenvectors and . Let P be the matrix having those eigenvectors as columns, and let D be the diagonal matrix with the eigenvalues –1 and –6 as its diagonal elements. Then and so .
Let . Then and . Those are simple harmonic motion equations, with solutions , .
Finally, , giving the solution