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..

Printable View

- May 3rd 2010, 10:19 AMMistOperator method help
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.. - May 3rd 2010, 11:43 AMOpalg
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