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.