Solving First-Order Differential Equations

Variable Separable Method

Used when the equation can be rearranged so that all $x$ terms are on one side and all $y$ terms on the other, then integrated:

$$\int g(y)\,dy = \int f(x)\,dx$$

Linear Differential Equations

An equation of the form $\dfrac{dy}{dx} + Py = Q$ is solved using an integrating factor.