# Diff. eq. help

1. Nov 6, 2006

### scienceman2k9

For this problem I don't think I am setting up the linear system right:

Two tanks containing 500 gal of salt solution. Pure water pours into the top tank @ 5gal/s. Salt solution pours out of the bottom of the tank and into the tank bellow @ 5 gal/s. There is a drain @ the bottom of the second tank, out of which the solution flows @ a rate of 5 gal/s. @ t=0 there is 100 lbs of salt present in the first tank and zero pounds in the tank immediately below.

Ok, so obviously the volume in the tanks is constant. also, if i let x1(t) and x2(t) be the amount of salt in the respective tanks....X1(0)=100 x2(0)=0

Now I need x'1 and x'2....which I think i may be doing wrong.

I have: x'1=(-5/500)x1 and x'2=(5/500)x1-(5/500)x2

If i factor out a 1/500 and solve the matrix I get a single eigenvalue of -5......but when I find the nullspace I get the v1 and v2 equal to zero which makes no sense. I was thinking that the negative sign on the x'1 equation might not be right, but if I drop that sign and solve the matrix again, I get complex eigenvalues.

Any guidance would be great.

2. Nov 6, 2006

### Office_Shredder

Staff Emeritus
You didn't post a question, just a scenario. What exactly are you trying to find?

3. Nov 6, 2006

### scienceman2k9

an expression for the content of salt in each tank over time, since tis an initial value problem