Question

Show that the function satisfies the heat equation.

Answer 1

What's the problem?

Answer 2

\[\frac{ ∂z }{ ∂t }=c^2\frac{ ∂^2z }{ ∂x^2 }~~~~~~~~(c >0, constant)\]

Answer 3

It's asking for a demonstration. Find both derivatives and check it out.

Answer 4

Question:
\[z=e^{-t}\sin(\frac{ x }{ c })\]

Answer 5

Oh i see, Thanks!

Answer 6

\[\frac{ ∂z }{ ∂t }=-e^{-t}\sin(\frac{ x }{ c })\]

For the other one, how do i get c^2 into the mix? @tkhunny

Answer 7

Just put it in. Simply substitute the two derivatives into the formula and see what happens.

Answer 8

ah, okay thanks.