Ok, I am unable to figure out the following problem.
Problem:
The following equation is used in the definition of a flow line: x'(t) = F(x(t))
Calculate the flow line x(t) of the given vector field F that passes through the indicated point at the specified value of t.
F(x,y) = -xi + yj; x(0) = (2,1)
The way I began this problem is to have x(t) = (x(t), y(t)) and then x'(t) = (x'(t), y'(t)). Then I don't know how to proceed. I tried equating components like so:
x'(t) = -x
y'(t) = y
But...that doesn't appear to work. Thanks for any help. I know my method is wrong because the next problem is similar, but I am not getting the same answer.