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 linex(t) of the given vector fieldFthat 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 havex(t) = (x(t), y(t)) and thenx'(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.