Here's the question. Ive got NO clue how to do it. It's from a tutorial and I'd love to have it done so I can prepare for the tests at the end of the year.
Cheers in advanced
Differentiate the second equation again with respect to t. Then substitute from the first into what you now have to get rid of the derivative of x, and then from the second to get rid of x. This will leave you with a second order linear constant coefficient ODE in y. Solve that and use the solution in the first equation to solve for x.
CB
On of the difficulties with not showing work at all is that we do not know which of possibly many methods of solving a particular problem you are familiar with. Captain Black suggested one method and apparently that works for you. Excellent.
I might be inclined to write this as the matrix equation
$\displaystyle \frac{d\begin{bmatrix}y_1 \\ y_2\end{bmatrix}}{dx}$$\displaystyle = \begin{bmatrix} 1 & -2 \\ 2 & 1\end{bmatrix}\begin{bmatrix}y_1 \\ y_2\end{bmatrix}$
and find the eigenvalues and eigenvectors of that 2 by 2 matrix.