The equation is:
dy/dx=y+2
The answer is y=Ce^{x}-2
Can anyone explain this?
If you also want to see why write
the equation is seperable and can be written as
$\displaystyle \int \frac{dy}{y+2} = \int dx$
so
$\displaystyle \ln (y+2) = x + c $
then taxing the exp of both sides and writing the arbitrary constant as C = ln c gives the solution as you have it
Or you can check the answer by taking the derivative of it:
$\displaystyle \frac{d}{dx} y(x) = Ce^x$
So you put this back into the differential equation:
$\displaystyle Ce^x = [Ce^x - 2] + 2$
It turns out to be true.