# 2.2 | Separable Equations

If the right-hand side of the equation
$$\frac{dy}{dx} = f(x,y)$$
can be expressed as a function $$g(x)$$ that depends only on $$x$$ times a function $$p(y)$$ that depends only on $$y$$, then the differential equation is called separable.
Method for Solving Separable Equations
To solve the equation
$$\frac{dy}{dx} = g(x)p(y)$$
multiply by $$dx$$ and by $$h(y):= 1/ p(y)$$ to obtain
$$h(y) \; dy = g(x) \; dx.$$
Then integrate both sides:
\begin{aligned} \int h(y) \; dy & = \int g(x) \; dx \\ H(y) & = G(x) + C \end{aligned}
where we have merged the two constants of integration into a single symbol $$C.$$ The last equation gives an implicit solution to the differential equation.