Numerical analysis question.

Question description

Need help with the question in attachment.
I’ve done part A need help with part B.
That’s what I have so far. Now, my question is trying to make this explicit form for U^n I tried solving it like the example in my notebook, but I’m getting confused with the initial conditions because it’s u(t=0)=c, but then my general solution only depends on n, not t?

Numerical analysis question.

Question description

Need help with the question in attachment.
I’ve done part A need help with part B.
That’s what I have so far. Now, my question is trying to make this explicit form for U^n I tried solving it like the example in my notebook, but I’m getting confused with the initial conditions because it’s u(t=0)=c, but then my general solution only depends on n, not t?

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