Consider the following code:
Element[f, Reals] && Element[\[Beta], Reals] &&
Element[\[Alpha], Reals] && Element[n, Reals] &&
Element[\[Epsilon], Reals] &&
\[Alpha] > 0 && \[Beta] > 0 && \[Mu] > 0 && \[Epsilon] > 0 &&
f > 0 && n > 0
f := 1 - Exp[-\[Beta] (1 - Exp[-\[Alpha]\[Epsilon]])^n]
DSolve[f''[\[Epsilon]] == 0, f[\[Epsilon]], \[Epsilon]]
I get the following error message :
DSolve::ivar: 1-E^(-(1-Power[<<2>>])^n \[Beta]) is not a valid variable.
What is my mistake? What is the correct method?
You gave f a value so it cannot be a dependent variable (the message pretty much states this). Maybe try Clear[f] before running the DSolve.
Thanks. I am a newcomer to mathematica.
Yes, your solution did not lead to the old error. But I still do not understand many things. You say that I gave f a value. I was just trying to define my function. Why did Clear not erase the definition?
I will try again with a function where I know the answer. This will hopefully help me to learn what I should do.
I should get x0 as the solution for f''[x]==0. The slope at this point should be U/(4*C). How do I get this with mathematica. How should I handle C and C? I don't understand what they mean.