1. ## DE trinomial?

First homework of the semester hits me with this:
Which of the following pairs of functions is a solution of the given system of differential equations on the interval ?

I don't want the answer! I do notice that "e" is involved.
I tried setting each equation = to x or y to substitute...fail
I tired to solve for dt and substitue...fail
I tried "coupled diff eq", but due to 3 variables...fail
Lastly, tried to seperate the variables so that I could get a dx/x, but the dt variable kept tripping me up!

2. ## Re: DE trinomial?

Originally Posted by diffyQ
First homework of the semester hits me with this:
Which of the following pairs of functions is a solution of the given system of differential equations on the interval ?

I don't want the answer! I do notice that "e" is involved.
I tried setting each equation = to x or y to substitute...fail
I tired to solve for dt and substitue...fail
I tried "coupled diff eq", but due to 3 variables...fail
Lastly, tried to seperate the variables so that I could get a dx/x, but the dt variable kept tripping me up!
Dear diffyQ,

To these type of Linear Homogeneous systems of Ordinary differential equations you should use the Eigenvalue method.

In this case the two differential equations could be written as,

$\frac{d\underline{X}}{dt}=\left(\begin{array}{cc}1 &3\\5&3\end{array}\right)\underline{X}\mbox{ where }\underline{X}= \left(\begin{array}{c}x\\y\end{array}\right)$

$|\underline{A}-\lambda\underline{I}|=0$

$\Rightarrow\left| \left(\begin{array}{cc}1&3\\5&3\end{array}\right)-\lambda \left(\begin{array}{cc}1&0\\0&1\end{array}\right) \right|= 0$

$\Rightarrow\left| \begin{array}{cc}1-\lambda & 3\\5& 3-\lambda \end{array} \right| = 0$

Hope you can continue form here.