Let f:R->(0,infinity) be positive, real analytic function such that f'(x) = f(x)...
...for all real x. Show that? f(x) = C*e^x for some positive constant C. The hint in the problem is that there are 3 different ways to do this, using logarithm function, using e^(-x) and using power series. but only one proof is needed.
...for all real x. Show that? f(x) = C*e^x for some positive constant C. The hint in the problem is that there are 3 different ways to do this, using logarithm function, using e^(-x) and using power series. but only one proof is needed.
