Answer
$\bf False$.
Work Step by Step
$\bf False$.
For this equation to be separable we would have to able to write $x+y$ from the equation $y'=x+y$ in the form of $f(x)g(y)$ where $f(x)$ is function in $x$ only and $g(y)$ is a function of $y$ only, which is impossible to write.