# How can i find equilibrium points of 2 ODEs?

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Volkan Yangin on 17 Nov 2020
Answered: John D'Errico on 17 Nov 2020
Hi,
I have 2 ODEs like this:
syms x1 x2
ode1=- 10*x2 - (9668*sin((pi*((317467494955027*(18*x1 - (2961*x2)/125))/(1125899906842624000*pi) + (11691*atan((317467494955027*(18*x1 - (2961*x2)/125))/(1125899906842624*pi) + 2222272464685189/28147497671065600))/(50*pi) + 2222272464685189/28147497671065600000))/180))/5125 - (9668*sin((pi*((11691*atan((317467494955027*(18*x1 - 180*u + (3339*x2)/125))/(1125899906842624*pi) + 2222272464685189/28147497671065600))/(50*pi) + (317467494955027*(18*x1 - 180*u + (3339*x2)/125))/(1125899906842624000*pi) + 2222272464685189/28147497671065600000))/180))/5125 - 236/1025
ode2= - (4771158*sin((pi*((317467494955027*(18*x1 - (2961*x2)/125))/(1125899906842624000*pi) + (11691*atan((317467494955027*(18*x1 - (2961*x2)/125))/(1125899906842624*pi) + 2222272464685189/28147497671065600))/(50*pi) + 2222272464685189/28147497671065600000))/180))/1665625 - (5380242*sin((pi*((11691*atan((317467494955027*(18*x1 - 180*u + (3339*x2)/125))/(1125899906842624*pi) + 2222272464685189/28147497671065600))/(50*pi) + (317467494955027*(18*x1 - 180*u + (3339*x2)/125))/(1125899906842624000*pi) + 2222272464685189/28147497671065600000))/180))/1665625 - 4956/13325
Is there any way to find the equilibrium points of them?
Thx!

John D'Errico on 17 Nov 2020
You have a system of ODEs. An equilibrium point is where the derivative is zero.
So just use solve, applied to the derivatives, thus solving for the point(s) where dx1/dt==0, dx2/dt==0.
If solve does not find a solution, (as I suspect it may fail here, finding no analytical solution) then use a tool such as vpasolve or fsolve.