Final answer:
The given differential equation is a nonlinear differential equation.
Step-by-step explanation:
The given differential equation is (1 + ye^0)dx + (2y + xe^(xy))dy = 0.
To determine the type of this differential equation, we can look at the coefficients of dx and dy. If the coefficients are functions of x and/or y, then it is a nonlinear differential equation. In this case, both coefficients are functions of x and y, so the given differential equation is a nonlinear differential equation.