Octave ODE’s

Here is an example of a single first-order differential equation:

function xdot = f(x,t)
xdot(1)=-x(1);
endfunction;
x0=[1];
t=linspace(0,6,50)’;
x=lsode(“f”,x0,t);
plot(t,x)

Here is a system of differential equations;
both dependent variables are shown in the picture;

function xdot = f(x,t)
xdot(1)=-.5*x(2);
xdot(2)=x(1);
endfunction;
x0=[0;2];
t=linspace(0,10,50)’;
x=lsode(“f”,x0,t);
plot(t,x)

The first example is solving ${dxover dt}=-.5 x$ with $x(0)=1$ , on $0leq tleq 6$ .

The second example is solving

${dx_1over dt}=-.5 x_2$ and ${dx_2over dt}=x_1$ with $x_1(0)=0$ and $x_2(0)=2$ , on $0leq tleq 6$ .

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