1. The problem statement, all variables and given/known data We know that y = Aex is the solution to the initial value problem dy/dx = y; y(0) = A. This can be shown by solving the equation directly. The goal of this problem is to reach the same conclusion using power series. Method: Let y be a solution to the initial value problem, and suppose y has the power series representation y(x) =the sum from n= 0 to n= infinity of (an)(x^n) which equals a0 + a1x + a2x^2 + ... First finnd a0. Next, take the term-by-term deriviative of the series to find a power series representation for dy/dx . Using the fact that dy/dx = y, obtain a formula which shows how an is related to an-1 for n >1. From this, find an explicit formula for an. Finally, use the known power series representation for e^x to conclude that y(x) = Ae^x 3. The attempt at a solution I know an = f(n)(0)/n! And I know the function is a power series centered at 0. but I don't really know where to go from there? i just don't know where to start on this. please help. if I see how to get started, I will be able to understand. I did try, but I don't know what to do!