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(s^2 + 1)f '(s) + s f(s) = 0

First I isolated for f '(s), which gave me:

f '(s) = -s f(s)/(s^2 + 1)

Then,

d f(s)/ds = -s f(s)/(s^2 + 1)

so, d f(s) = (-s f(s)/(s^2 + 1))ds

Integrating I get:

f(s) = -F(s)ln(s^2 + 1)/2 + C, where F(s) is the antiderivative of f(s) and C is a constant of integration.

Did I do any of that correctly??!!??