The logistic equation is y/= y(1-y). (a) Let c be a constant. By hand, plug the...

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The logistic equation is y/= y(1-y). (a) Let c be a constant. By hand, plug the function Yg(x) = ez c+e into both sides of the logistic equation to verify that y, (r) is a solution. (b) Using the general solution y(x) from part (a), find c to obtain the solution to the initial value problem (IVP) y = y(1-y), y(0) = . (c) Using Mathematica's Plot function, plot the solution y(x) from part (b) on the interval * € [0,4]. The logistic equation is y/= y(1-y). (a) Let c be a constant. By hand, plug the function Yg(x) = ez c+e into both sides of the logistic equation to verify that y, (r) is a solution. (b) Using the general solution y(x) from part (a), find c to obtain the solution to the initial value problem (IVP) y = y(1-y), y(0) = . (c) Using Mathematica's Plot function, plot the solution y(x) from part (b) on the interval * € [0,4].