Separable Differential Equations

#calc/concept
Another form of differential equations, which has its own way of being solved.

A differential equation of the form $\frac{dy}{dx}=f(y)g(x)$ is separable. In order to solve this equation, we have to separate it. We separate the variables by putting the $x$s on one side and the $y$s on the other: $\frac{1}{f(y)}dy=g(x)dx$. Then we can simply integrate each side. Sometimes, an initial condition will be given; in these cases, you can solve for $C$.

Video