Given a differential equation, you can find and analyze its' equilibrium solutions. To find the equilibrium solutions, you find what y values make the equation equal to zero. Once you have the specific y-values, you can use a phase line to analyze the y-values' stability. To better determine if the equilibrium solution is stable or unstable, I have provided examples below.
Helpful tip: If on the phase line prior to the solution is decreasing and after the solution is increasing, it is unstable (looks like a u). Swap those directions and it would be stable (looks like an upside-down v)
Steps: 1. Evaluate the differential equation to find values that make it equal to zero 2. Once you have found the values, put them on a phase line, each with a value greater and less than next to the solved value on the line 3. Determine whether the neighboring values increase or decrease (positive or negative) by plugging them into the original differential equation 4. Make conclusions based off of what the neighboring values do