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:
$y' + x~\sqrt{y} = x^2$
Because of the $\sqrt{y}$ in the equation, this differential equation is not linear.