Answer
This differential equation is not 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:
$\frac{dR}{dt} + t~cos~R = e^{-t}$
Because of the $~~cos~R~~$ in the equation, this differential equation is not linear.