Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I have a question that asks to draw the direction field for the set of linear systems.

$$\begin{align} \frac{d\,x}{dt} &= -x + y + 1 \\ \frac{d\,y}{dt}&=x+y+3\end{align}$$

My attempt:

What I did first was set the system in the form of $d(Q)/dt = KQ + b$, then I found the critical points which was at $[2,1]$ and then I chose an arbitrary point in the plane, lets pick $[1,2]$, and set it as my Q and then solved and found the vector $[1,3]$ to be associated to that point, but this is where I have a problem. How will this vector be plotted? I am on point $[1,2]$ and the tangent vector is $[1,3]$ but how can I draw this? Will it go up 1 unit and right 3?

share|improve this question
add comment

1 Answer

up vote 1 down vote accepted

See here for an explanation of what a direction field is.

At the point $(a,b)$, the tangent vector is $v=[-a+b+1,a+b+1]^T$, from the ODE system that you give.

Specifically at the point $(1,2)$, the tangent vector is $v=[0,4]^T$, which is a vector parallel to the $x$-axis ($0$ up and $4$ to the right). This process is then repeated for all points in the plane.

share|improve this answer
    
Apparently the vector <1,3> is wrong though because in my book it shows that the direction field is flat, almost like a 0 slope at point (1,2). –  Q.matin Oct 1 '12 at 6:53
1  
I will edit my post to update. I assumed you were correct. –  Daryl Oct 1 '12 at 7:49
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.