(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Draw a direction field for the following differential equation:

[tex]x=c_1\left(

\begin{array}{c}

1 \\

1

\end{array}

\right)e^t+c_2\left(

\begin{array}{c}

1 \\

3

\end{array}

\right)e^{-t}[/tex]

2. Relevant equations

N/A

3. The attempt at a solution

With a single differential equation, all you do is choose arbitrary x and y values and plug them into the differential equation. What you get is a slope, so you draw a little arrow with this slope at the point (x,y).

However, I don't know how to deal with a system of equations. If I choose arbitrary values for x and t, then I get multiple slopes. I can only draw one arrow at the point (x,t), so what do I do with multiple slopes?

Thank you in advance for your help!

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# Homework Help: Direction Fields for Systems of Differential Equations

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