Question

When solving a 1-Dimensional heat equation using a variable separable method, we get the solution if ______________

(a) k is positive

(b) k is negative

(c) k is 0

(d) k can be anything

I got this question in an interview for internship.

The above asked question is from Solution of PDE by Variable Separation Method in division Applications of Partial Differential Equations of Engineering Mathematics

Answer 1

Right answer is (b) k is negative

Easy explanation: Since this is a heat equation, the solution must be a transient solution, that is it should decay as time increases. This happens only when k is negative and the solution comes out to be (c’’cospx + c’’’sinpx) (c e^-c^2 p^2 t).