Question

solve for T.

(d^2)/(dx^2)*T+(d^2)/(dy^2)*T=-2*(pi^2)*sin(pi*x)*sin(pi*y)

I think you have to do method of separation of variables and then some eigenvalue/function thing...? But I'm not sure of the exact steps.

Answer 1

Can I walk you through it instead of just doing it for you?

Answer 2

sure, grateful for any help!

did i get the method correct?

Answer 3

To be honest, I don't know the names of stuff, but you're correct that you have to somehow separate out the T.

If you look at the equation you're given, you see that there are two terms that have T in them, right?

Answer 4

yes

i thought maybe i could do a double integral of (d^2/dx^2)*T=sin(pi*x)
and do an analogous equation for the y and then add the two answers

Answer 5

oh wait, is dx a single variable?

Answer 6

I thought this was just algebra.

Answer 7

i mean it as second derivative of T when I write (d^2/dx^2)*T

Answer 8

partial derivatives

Answer 9

oh, okay. I get it now. I just didn't understand the notation written out like that I guess. So yes, double integral is the way to go.

Answer 10

and then just add the two solutions? sorry - dont have a math textbook with me. i think i need a quick refresher.

Answer 11

but remember that when you write the double integral, you have to make sure to include everything on one side, not just the parts you want.

Answer 12

i see. so on the right hand side, i keep the same but then take the double integral with respect to x, and then respect to y?

Answer 13

hold on, this is more complicated than I originally thought, so I'm doing it out on paper first to see how it works.

Answer 14

so I'm not sure exactly how to do this, but I think I can tell you if you're wrong/why something wouldn't work.

Answer 15

ok. so this is what i did before i get stuck:
1. the solution is some generalized u=X(x)Y(y)
2. plug this general solution into the original equation
3. i get: y((d^2/dx^2)*x)+((d^2/dx^2)y)*x = -2*(pi^2)*sin(pi*x)*sin(pi*y)
4. stuck! :)

Answer 16

it's ok i think i'll just move on to something else

thanks for your time and effort! i appreciate it. :)

Answer 17

yeah, sorry about that.