I'm trying to show that the following initial-value problem
$$ \frac{x^{\prime}\left(t\right)}{1 + x \left(t\right)^{2}} + \frac{x\left(t\right)}{t} = 1 $$
with initial condition $x\left(t_{0}\right) = a > 0$ has a unique solution for $t \geq t_0 > 0$.
I know how to work with homogenous equations only, I tried to reorder the equation but failed. How can I approach such question?