When solving the differential equation:
$dy/dx = y^2$, with $y(0) = 1$
$y = 1/(1-x)$ as the solution.
The problem asks then for an explanation to why $x=3/2$ is an invalid point to consider when graphing the solution.
The solutions manual says that although the formula for $y$ makes sense at $x=3/2$:
$y(3/2) = -2$;
it is not consistent with with the rate of change interpretation of the differential equation. It continues saying that the function is defined, continuous and differentiable for $-\infty < x < 1$.
It is clear to me that at $x=1$ both $y$ and $dy/dx$ are undefinded, but I cannot understant why the solution y does not apply for values of $x$ higher than $1$.