Solving ODE with two variables and derivatives

Question

Nick987 2020-5-8

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评论： Suhaib Salah 2021-11-8

Hi guys i need help solving this system. I symplified the system to its basics. I want to get and plot y(t) in the end. My system tells me it doesnt know r. How can i tell the system to solve the ode of r within the ode of y? Where do I put the r0 in? I am an beginner in Matlab though :D Thank you very very much!! Stay safe and healthy you all!

initial conditions: y0 and r0

parameters: B,C,D

A is a function of y

......

tspan=linspace(0,10); %for both integrals y and r

[t1,y1] = ode45(@(t,y) Simulation(t,B,C,D,E,F), tspan, y0);

.....

function dydt = Simulation (t,B,C,D,E,F)

drdt = -C*(B+D);

A= E-y*F;

dydt = A- ( (y/r) * drdt);

end

...

plot(t1,y1)

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Answer 1

Guru Mohanty 2020-5-11

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Hi, I understand you are trying to solve the system of two variable ODE. Numerically, you can do this using ode45. Here is the modified code for it.

clc;clear all;
% Initial Conditions
y0=0;
r0=0;
% Constant Declaration
B=1; C=1; D=2; E=1; F=1;
con1=-C*(B+D);
tspan=linspace(0,10); %for both integrals y and r
[t1,z1] = ode45(@(t,z)Simulation(t,z,E,F,con1), tspan, [r0;y0]);
plot(t1,z1);
function dOutdt = Simulation (t,z,E,F,con1)
dOutdt=zeros(2,1);
y=z(1);
r=z(2);
dOutdt(1) = con1;
A= E-y*F;
dOutdt(2) = A - ( (y/r)  * dOutdt(1));
end