Question

If f'(x)=-f(x) and f(1)=1, what's f(x)? (Answer: e^(1-x))

Answer 1

That is correct.

Answer 2

But I don't know how to do the problem.

Answer 3

y'=-y, y'+y=0
Auxiliary equation: r+1=0, r=-1
General solution: y=ae^(-x)
f(1)=1: ae^(-1)=1, a=e.
Therefore solution: y=e*e^(-x)=e^(1-x)

Answer 4

Thank you.

Answer 5

no problem :)