# Thread: Solving a System (Best Explanation i Have)

1. ## Solving a System (Best Explanation i Have)

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.

2. Originally Posted by exphate
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.

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

3. Thanks CB. I took what I got after your post, and have gotten answers out. Im gunna see the tutor later this week to have them checked

4. 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.