Simple DE....but lack of practice.

Hey,

I haven't looked at differential equations for some years... and I'm having trouble with two really simple ones....(Speechless)

$\displaystyle \frac{dx}{dt} = (x + 2), x(0) = 1 $ ........ODE (1)

and $\displaystyle \frac{dy}{dt} = 2y, y(0) = 1$............ ODE (2)

The text I'm looking at says the answers for ODE (1) and ODE (2) should be $\displaystyle x + 2 = 3e^t$ and $\displaystyle y = e^{2t}$ respectively.

I thought the solutions (not imposing the initial conditions are) for each of the conditions are

$\displaystyle xt + 2t$ and $\displaystyle 2yt$ respectively.

I must be doing this incorrectly. Do I use separation of variables?

$\displaystyle \int \frac{dx}{x+2} = \int \ dt$

and

$\displaystyle \int \frac{dy}{y} = \int 2 dt$ ?

If so, how do I integrate $\displaystyle \int \frac{dx}{x+2} $ and $\displaystyle \int \frac{dy}{y} $ ?

Thanks