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Find the three zeros seen above more accuractely PkkjeDFHNiItSSdmc29sdmVHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2JEkiZkdGJC9JInhHRiQ7ISIiIiIh JCErJTRueDIlISM1 PkkjeDJHNiItSSdmc29sdmVHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2JEkiZkdGJC9JInhHRiQ7IiIhIiIi JCIrQyJmIVtyISM1 PkkjeDNHNiItSSdmc29sdmVHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2JEkiZkdGJC9JInhHRiQ7IiIlIiIm JCIrR1plMVYhIio= Considering the sign of the derivative of f at the equilibrium points seen from the graph, x2 is stable and x1 and x3 are unstable. Q#3 QyQ+SSdpbXByZWxHNiIvLCoqJkkieEdGJSIiIkkieUdGJSIiJEYqKiZGKSIiI0YrRi5GKiomRilGLEYrRipGKiEiJEYqIiIhRio= LywqKiZJInhHNiIiIiJJInlHRiYiIiRGJyomRiUiIiNGKEYrRicqJkYlRilGKEYnRichIiRGJyIiIQ== QyQtSSV3aXRoRzYiNiNJJnBsb3RzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlISIi LUktaW1wbGljaXRwbG90RzYiNiVJJ2ltcHJlbEdGJC9JInhHRiQ7ISIjIiIkL0kieUdGJEYp 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 Q#4 Specify the DE and the initial condition, then use dsolve to find the solution QyQ+SSNkZUc2Ii8tSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUkidUdGJTYjSSJ0R0YlRi4sJiokRisiIiMiIiIhIiJGMkYy Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1RzYiNiNJInRHRilGKywmKiRGJyIiIyIiIiEiIkYv QyQ+SSNpY0c2Ii8tSSJ1R0YlNiMiIiEjIiIiIiIjRiw= Ly1JInVHNiI2IyIiISMiIiIiIiM= LUknZHNvbHZlRzYiNiQ8JEkjZGVHRiRJI2ljR0YkLUkidUdGJDYjSSJ0R0Yk Ly1JInVHNiI2I0kidEdGJSwkLUkldGFuaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLCZGJyIiIi1JKGFyY3RhbmhHRis2IyNGMCIiIyEiIkY2 Isolate the expression on the LHS above as the solution. QyQ+SSVzb2xuRzYiLUkkcmhzRyUqcHJvdGVjdGVkRzYjSSIlR0YlIiIi LCQtSSV0YW5oRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJkkidEdGKCIiIi1JKGFyY3RhbmhHRiU2IyNGLCIiIyEiIkYy The range of the plot was not specified, I tested a few things until I saw that it was tending to an equilibrium point. 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