simple problem

[circa415]

Given x(0)=-2, y(0)=1, x'(t)=2x(t), y'(t)=-2y(t), solve for x(t) and y(t)

I plugged this into mathematica and got -2e^(2t)=x(t) and e^(-2t) = y(t)

I notice that x'(t) = 2x(t) means that x(t) has to be e^t and there must be a coefficient (2) in front of the t because the only derivative that has this property is e^x. And the coefficient in front of e will be given by x(0). But is there a "method" that I can go about doing this? or can you only do it by observation?

[stunner5000pt]

for the x(t) you forgot to include the x(0) part in the formation of the x(t) function, you need to add something to it to be true for x(0)

Similarly for the y(0)