Chapter 2.2, Problem 41E

Often a radical change in the form of the solution of a differential equation corresponds to a very small change in either the initial condition or the equation itself. In Problems 39-42 find an explicit solution of the given initial-value problem. Use a graphing utility to plot the graph of each solution. Compare each solution curve in a neighborhood of (0, 1).

41. $\frac{dy}{dx}={(y-1)}^2+0.01$, y(0) = 1