- #1
Qyzren
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Hi guys, i have 4-coupled ode's that are giving trouble
(1) \frac{dy_1}{dt}=y_2y_3-\mu y_1, \hspace{1cm} \\(2) \frac{dy_2}{dt}=y_1y_4-\mu y_2, \hspace{1cm} \\(3) \frac{dy_3}{dt}=1-y_1y_2, \hspace{1cm} \\(4) \frac{dy_4}{dt}=1-y_1y_2
I need to show that the steady state solutions are
y_1=\pm k, y_2=\pm k^{-1}, y_3=\mu k^2, y_4 = \mu k^{-1} where \mu (k^2-k^{-2})=A a const.
now in an earlier part of the question, I was able to show that y_3-y_4=A.
But trying to solve these coupled ODE's is giving trouble. I tried solving this in mathematica using DSolve as well, and mathematica doesn't seem to know how to do it either.
mathematica code:
\text{DSolve}\left[\left\{\text{y1}'[t]==-\mu \text{y1}[t]+\text{y2}[t] \text{y3}[t],\text{y2}'[t]==-\mu \text{y2}[t]+\text{y1}[t] \text{y4}[t],\text{y3}'[t]==1-\text{y1}[t] \text{y2}[t],\text{y4}'[t]==1-\text{y1}[t] \text{y2}[t]\right\},\{\text{y1}[t],\text{y2}[t],\text{y3}[t],\text{y4}[t]\},t\right]
PS: how do i get each of the differential equations on a new line? \\ and \newline didn't work.
each of the ODE's starting with the derivative should be on a new line
(1) \frac{dy_1}{dt}=y_2y_3-\mu y_1, \hspace{1cm} \\(2) \frac{dy_2}{dt}=y_1y_4-\mu y_2, \hspace{1cm} \\(3) \frac{dy_3}{dt}=1-y_1y_2, \hspace{1cm} \\(4) \frac{dy_4}{dt}=1-y_1y_2
I need to show that the steady state solutions are
y_1=\pm k, y_2=\pm k^{-1}, y_3=\mu k^2, y_4 = \mu k^{-1} where \mu (k^2-k^{-2})=A a const.
now in an earlier part of the question, I was able to show that y_3-y_4=A.
But trying to solve these coupled ODE's is giving trouble. I tried solving this in mathematica using DSolve as well, and mathematica doesn't seem to know how to do it either.
mathematica code:
\text{DSolve}\left[\left\{\text{y1}'[t]==-\mu \text{y1}[t]+\text{y2}[t] \text{y3}[t],\text{y2}'[t]==-\mu \text{y2}[t]+\text{y1}[t] \text{y4}[t],\text{y3}'[t]==1-\text{y1}[t] \text{y2}[t],\text{y4}'[t]==1-\text{y1}[t] \text{y2}[t]\right\},\{\text{y1}[t],\text{y2}[t],\text{y3}[t],\text{y4}[t]\},t\right]
PS: how do i get each of the differential equations on a new line? \\ and \newline didn't work.
each of the ODE's starting with the derivative should be on a new line
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