# Linear algebra - System of differential equations

by pyroknife
Tags: algebra, differential, equations, linear
 P: 379 I'm a bit confused on how to do this problem, here is what I have. Part a) I must set up the set of linear differential equations with the initial values. Using the balance law gives y0'=0.2+0.1-0.2-0.1=0 The other 2 net rate of change would be equal to 0 as well. But...I don't think I did that right. Attached Thumbnails
 HW Helper Sci Advisor Thanks P: 7,864 I would think the flows would be proportional to the temperature differences. If so, the numbers shown on the diagram are coefficients for that. You will need to invent variables for the three temperatures as functions of time, yes? (It's not clear to me which box is which in the diagram. Hope it is to you.)
 PF Patron Sci Advisor Thanks Emeritus P: 38,400 For example, "0" is losing heat to "1" at 0.2 times its temperature and is losing heat to "2" at 0.1 its temperature. It is losing heat at a total of $0.3y_0$. But it is gaining heat from "1" at $0.2y_1$ and from "2" at $0.1y_2$. The equation is $y_0'= 0.2y_1+ 0.1y_2- 0.3y_0$ and similarly for the others.
P: 379

## Linear algebra - System of differential equations

Oh thank you guys, I see what I need to do.

Yeah, I was also confused what area each box was referring to. I'm assuming 1 represents the 1st floor and 2 the second. That leaves 0 as the outside, but I could be wrong.
 P: 379 Revisiting this problem. Would the initial conditions be y Spoiler 0 (0)=0 y1(0)=70 y2(0)=60 ?
 HW Helper Sci Advisor Thanks P: 7,864 Sure. What ODEs do you get?
 P: 379 I got Y0'=-0.3y0+0.2y1+0.1y2 Y1'=0.2y0-0.7y1+0.5y2 Y2'=0.1y0+0.5y1-0.6y2 Y0(0)=0 Y1(0)=70 Y2(0)=60 The eigenvslues are really ugly
HW Helper
Thanks
P: 7,864
 Quote by pyroknife I got Y0'=-0.3y0+0.2y1+0.1y2
I don't think heat escaping the house will do much to outside temperature.
 Y1'=0.2y0-0.7y1+0.5y2 Y2'=0.1y0+0.5y1-0.6y2
There's an assumption in there that the two parts of the house have the same specific heat. I suppose you have to assume that.
 P: 379 Hmm I don't think we're supposed to think too Much about thermodynamics for this problem. Do those equations and ICs look right?
HW Helper