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in this video were going to find bifurcation values for a one-parameter family of autonomous differential equations and were going to draw phase lines before and after each bifurcation value so suppose we have a one-parameter family given by this formula so what we want to do is find the bifurcation values which are the values of a for which the number or type of equilibrium points of this differential equation changes suddenly theres always several approaches to doing this some are algebraic and some are graphical and in this case were going to see pretty quickly that were gonna have to resort to graphical approaches so one approach is to algebraically determine what the equilibrium points of this guy are for arbitrary values of a so if I just fix a to be a single value and I look for equilibrium points Id be solving this guy and since this has an e to the y and and a y in it basically were not going to be able to solve this in any easy way so this algebraic approach of lookin