# how to solve non linear differential equations

3 views (last 30 days)
nune pratyusha on 3 Mar 2021
dx(t)/dt=y(t)
dy(t)/dt=-(1/r+g+a+b|x(t)|)y(t)/c-x(t)/(lc)
t=-0.05:0.01:0.05
r = 1430;
a = -0.0683;
b = 0.0676;
c = 36*10^-9;
g = -0.0676;
l=27
i want to plot phase portrait of (x(t),y(t)) and plots for (t,x(t)),(t,y(t))

Bjorn Gustavsson on 3 Mar 2021
Edited: Bjorn Gustavsson on 4 Mar 2021
Have a look at the help and documentation of ode45 and the numerous ode-examples.
In brief to solve this ODE-system write a matlab-function for the derivatives:
function dxdtdydt = your_ode(t,xy,pars)
r = pars(1);
a = pars(2);
b = pars(3);
c = pars(4);
g = pars(5);
l = pars(6);
y = xy(2);
x = xy(1);
dxdt = xy(2);
dydt = -(1/r+g+a+b*abs(x)*y/c-x/(l*c));
dxdtdydt = [dxdt;
dydt];
That ode you then integrate from some initial state over some time-period of interest
r = 1430;
a = -0.0683;
b = 0.0676;
c = 36*10^-9;
g = -0.0676;
l=27;
pars = [r,a,b,c,g,l];
t = -0.05:0.01:0.05;
x0y0 = [0,1]; % I wouldn't know.
[t,xy] = ode45(@(t,xy) your_ode(t,xy,pars),t,x0y0);
HTH
Bjorn Gustavsson on 5 Mar 2021
Well the solution does not look like a sine-wave. That is because I have yet another typo in the ODE, you will surely find it if you look close and read the code, and think about what you need to obtain an oscillating solution.

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