Answer
linear
Work Step by Step
Given $$u e^{t}=t+\sqrt{t} \frac{d u}{d t}$$
Rewrite the equation
$$ \frac{d u}{d t} -\frac{e^t}{\sqrt{t}}u =\frac{-t}{\sqrt{t}}$$
Then by comparing with the general from , we conclude that the equation is linear
