Consider the differential equation $y' = 1 - y^2$.
First, is $y(x) = 1$ the only constant solution?
I now want to solve the equation for the initial value problem $y(0) = y_0$, with $y_0 > 1$.
Also, what's the maximal interval the solution function can be defined on? How does it behave at the edges (potentially for $x \to ± \infty$)?
Thanks in advance. Differential equations are new to me and I have trouble on how to visualize and solve an equation like this.