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

This isn't really even a homework question..i've just been reviewing some general math concepts and this one has been driving me nuts..i haven't done math in a while.

At time t = 1, a particle is located at position (1,3). If it moves in a velocity field F(x,y) = <xy-2,y^2 - 10>, find its approximate location at time t = 1.05

2. Relevant equations

n/a

3. The attempt at a solution

I thought, maybe:

dx/dt = xy - 2 and dy/dt = y^2 - 10

So I can integrate, so x(t) = (1/2)x^2 * y - 2x + C and y(t) = (1/3)y^3 - 10Y + C and solving for the constants is trivial based on the initial conditions, but then I get totally confused. How do I put this in terms of T? And did I even do this right? It doesn't make sense to me that the position should be the function of a position. I must have done my integral wrong.

Can you guys help me out...really stuck.

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# Vector Fields

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