Mathematics — Real Analysis · picard-theorem-exponential-h-bound
Problem
Consider the equation f′(x)=f(x), from Example 6.3.3. Show that given any x0, any y0, and any positive h<1/2, we can pick α>0 large enough that the proof of Picard's theorem guarantees a solution for the initial condition f(x0)=y0 in the interval [x0−h,x0+h].