Question

While solving a partial differential equation using a variable separable method, we equate the ratio to a constant which?

(a) can be positive or negative integer or zero

(b) can be positive or negative rational number or zero

(c) must be a positive integer

(d) must be a negative integer

I have been asked this question in an international level competition.

My enquiry is from Solution of PDE by Variable Separation Method topic in chapter Applications of Partial Differential Equations of Engineering Mathematics

Answer 1

The correct option is (b) can be positive or negative rational number or zero

To explain: The constant can be any rational number. For example, we use a positive rational number to solve a 1-Dimensional wave equation, we use a negative rational number to solve 1-Dimensional heat equation, 0 when we have steady state. The choice of constant depends on the nature of the given problem.