# How can I graph a "system" of ODEs?

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Michael on 5 Jul 2012
I am trying to model a shape that is defined with multiple differential equations. For reference, the variables are x and y (from the normal Cartesian plane) and then S (arc length) and theta (angle of the arc length with the horizontal).
The equations are:
dtheta/dS = -sin(theta)/x + y - 2H (a constant)
dx/dS = cos(theta)
dy/dS = sin(theta)
I'm just wondering if MatLab has an easy way to do this. If not, how could I set up a modified Euler's Method to solve this?

Star Strider on 5 Jul 2012
Michael on 8 Aug 2012
Seen it. Didn't really help me. I've used ode45 on a 2nd order ODE, but have never used these with systems.

Star Strider on 8 Aug 2012
Edited: Star Strider on 8 Aug 2012
Is this what you want to do?
% dThXYdS(1) = theta(S), dThXYdS(2) = x(S), dThXYdS(3) = y(S)
H = 10;
dThXYdS = @(t,XYTh) [-sin(XThXY(1))/ThXY(2) + ThXY(3) - 2*H; cos(ThXY(1)); sin(XYTh(1))];
x0 = [0.1; 0.1; 0];
Tspan = [0:0.01:2]';
[T ThXY] = ode45(dThXYdS, Tspan, x0);
figure(8)
plot3(ThXY(:,1), ThXY(:,2), ThXY(:,3))
xlabel('X(S)')
ylabel('Y(S)')
zlabel('\Theta(S)')
grid
I have no idea what you intend for H or the rest, but this seems to work. I named the variable ThXY to denote the vector as [Theta(S); X(S); Y(S)].