Final answer:
The given differential equation is separable.
Step-by-step explanation:
A separable differential equation is a type of ordinary differential equation (ODE) that can be written in a form where the variables can be separated on opposite sides of the equation. This allows for the integration of each side independently, making it possible to find a solution to the differential equation.
The given differential equation is -y dy/dx + (x + (√xy) = 0.
To determine the type of the differential equation, we can check for certain properties. Since the equation contains only the dependent variable y and its derivative, but not the independent variable x, it is a separable differential equation. Therefore, the correct answer is option (c) separable.