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

Determine the vector in the direction field( in the form of < 1, ? >) correspond-

ing to the given point.

y' = 1 + 2ty at (2, 0), at (3, -2).

2. Relevant equations

3. The attempt at a solution

y'-2ty=1

p(t)=-2t ; u(t)=e^(-t^2)

e^(-t^2)-2te^(-t^2)=e^(-t^2)

e^(-t^2)=integral(e^(-t^2)dt)+c

I am confused where to go from here. I think I am supposed to set up the integral definitely. When i do from 0->0 I get c=2.

From here I am not sure where to go. Do I set up the integral from 0->1 (since I am trying to find a vector with t =1)? When I do this it comes out to <1, 2.63> What made me doubt this was how I am supposed to set up the problem at point (3,-2).

Do I plug in t=0 and for the integral do 0->1 ?

And plug in t=3 and do 3->4 integral ?

This does not really seem right though -.-

My weakness may lie in the fact that I have no notes on how to find a vector <1, ?>.

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# Determining vector in a direction field

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