Final answer:
The differential equation dy/dt + 11ty = -3eⁿ¹ is neither linear nor separable because of the non-linearity introduced by the term -3eⁿ¹, which is a function of y rather than t or a constant.
Step-by-step explanation:
The given differential equation is dy/dt + 11ty = -3eⁿ¹. A linear differential equation typically takes the form dy/dt + p(t)y = g(t), where p(t) and g(t) are functions of t only. However, for an equation to be separable, it should be possible to express it in the form N(y)dy = M(t)dt. In the given equation, the presence of the term -3eⁿ¹ introduces a nonlinearity because it is a function of y rather than a function of t alone or a constant. Moreover, the term cannot be separated into a product of a function of y and a function of t, meaning it is not separable. Therefore, the correct answer is E) It is neither linear nor separable.