I'm looking into solving the following integral equation:
$$y(x)=1+\int^{x}_{0}(\tanh s)y(s)ds$$
How can I go about turning this into a differential equation? i.e. of the form
$$y'(x)=f(y)$$ for some function $f$ so we can then apply $y(0)=1$ to deduce a solution by standard techniques for Differential Equations.