I have the following system of differential equations, and I am not able to understand the best way to go about them. I tried using a couple of functions like dsolve, ode45, etc., but most of them give errors that I am not able to understand.
x(1)=0.3; x(3)=0.9; y(1)=0.4; y(3)=0.8;
syms X1 X2;
num = ((x(3)-X1)-(X1-x(1)))*X1 + ((y(3)-X2)-(X2-y(1)))*X2;
den = sqrt((x(3)-X1)-(X1-x(1))^2 + (y(3)-X2)-(X2-y(1))^2);
Em = -A*(X1-x(1))*(x(3)-X1) - A*(X2-y(1))*(y(3)-X2) + p*num/den;
dXdt = [-diff(Em,X1); -diff(Em,X2)];
I would like to get X1 and X2 as a function of time. If I define syms X1(t) and X2(t), I get the error 'All arguments, except for the first one, must not be symbolic functions.' The above code, when run, gives me expressions in terms of X1 and X2. I need solutions of X1 and X2 in terms of t, where dX1dt = -diff(Em,X1), dX2dt = -diff(Em,X2).
Any help is appreciated. Thank you!