Answer
This differential equation is linear.
Work Step by Step
A first-order linear differential equation is one that can be put into the form:
$\frac{dy}{dx} + P(x)~y = Q(x)$
We can consider the given equation:
$y' - x = y~tan~x$
$y' - (tan~x)~y = x$
$\frac{dy}{dx} - (tan~x)~y = x$
Let $P(x) = -tan~x$
Let $Q(x) = x$
This differential equation is linear.