Question

Which of the following is true about the differential equation below?

dy/dt + 11ty = -3eʸ

A) It is separable.
B) It is linear without constant coefficients.
C) It is linear with constant coefficients.
C) It is both linear and separable.
E) It is neither linear nor separable.

Answer 1

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.