First order differential equations of the form $\dfrac{dy}{dx}~=~f(x)g(y)$ can be solved by separating the variables.

$\dfrac{dy}{dx} = f(x)g(y)$

$dy$ and $dx$ can be treated as variables and manipulated the usual way.

$\dfrac{1}{g(y)} dy = f(x)dx$

Integrate both sites with respect to $y$ and $x$ respectively.

$\displaystyle\int{\dfrac{1}{g(y)}} dy = \displaystyle\int{f(x)} dx$

The general solution to a differential equation will be in the form:

$y = F(x) + c$

If you know one point on the curve, $c$ can be solved and a particular solution can be obtained.