# 4 differencial equations problem

• Dec 12th 2006, 08:11 PM
4 differencial equations problem
P1. Find equilibrium pts. of model:

[da/dt] = [1a + 3b + 5]
[db/dt] [2a + 4b + 6]

P2. Find equilibrium pts. of model:

[da/dt] = [a - b]
[db/dt] [2a - b - (a^2)]

P3. Find equilibrium of this z(t) @ time t:

dz/dt = A - cB(((2D)/(BE))^(3/4))(z^(3/4)) (c is a constant)

P4. Linearize this model/equation and use least-squares fit (w/ given points) to estimate constants:

dz/dt = az - ab(z^2)

t : 0 1 2 3 4 5
z : 1.0 1.2 1.4 1.6 1.8 2.0

Good luck and tenx! :)
• Dec 13th 2006, 03:23 AM
Fredrik
P1. Put both derivatives =0 and subtract 2 times the first equation from the second to get an equation with only b. Then solve for b and use the result to find a.

P2. Again, both derivatives =0. The first equation becomes a=b. That result transforms the second equation into an equation with only one variable. Solve it.

P3. I'm assuming that A, B, D and E are also constants? Just put that expression =0 and solve for z(t).

P4. Again, the equation is "what you wrote"=0. Just divide both sides with z to simplify the equation.

If you want more help than that, I think you should show us what you've got so far.