Question

The one dimensional heat equation can be solved using a variable separable method. The constant which appears in the solution should be __________ *

1 point

Positive

Negative

Zero

Can be anything​

Answer 1

positive and positive

Answer 2

Answer:

The one-dimensional heat equation can be solved using a variable separable method. The constant which appears in the solution should be __________

Step-by-step explanation:

In cartesian system, consider the specific case of a function $\[u\left( {x,y,z,t} \right)\]$ of three spatial variables$\[\left( {x,y,z} \right)\]$ and time variable $\[t\]$.

Therefore, the heat equation is as follows

$\[ \Rightarrow \frac{{\partial u}}{{\partial t}} = \alpha \left( {\frac{{{\partial ^2}u}}{{\partial {x^2}}} + \frac{{{\partial ^2}u}}{{\partial {y^2}}} + \frac{{{\partial ^2}u}}{{\partial {z^2}}}} \right)\]$

where $\[\alpha \]$ is a positive coefficient called thermal diffusivity.

Hence, the correct option is (1) i.e. positive.