# plese help someone.I need to solve simultaneous differential eqns with multiple dependent variable.

1 view (last 30 days)
ajeet sahu on 5 Sep 2021
Commented: Paul on 6 Sep 2021
here is what I written to solve these eqns. I'm getting error.I don't have any initial conditions.Also I need to plot y1,y2 and y3.I'm still learning matlab and don't have idea how to solve this problem.
clc;clear;close;
%write given values
m1=1; m2=2; m3=3;
c1=3; c2=1;
k1=2; k2=2;
f1=5; f3=2;
%call the function named 'func'
[y1 y2 y3]=func(m1,m2,m3,c1,c2,k1,k2,f1,f3)
function [y1 y2 y3] =
func(m1,m2,m3,c1,c2,k1,k2,f1,f3)
%define variables
syms y1(t) y2(t) y3(t)
%write differential equations
eqn1=m1*diff(y1,t,2)==f1-c1*(diff(y1,t)-diff(y2,t))-k1*(y1-y2);
eqn2=m2*diff(y2,t,2)==-c1*(diff(y2,t)-diff(y1,t))-k1*(y2-y1)-c2*(diff(y2,t)-diff(y3,t))-k2*(y2-y3);
eqn3=m3*diff(y3,t,2)==-f3-c2*(diff(y3,t)-diff(y2,t))-k2*(y3-y2);
%solve these eqns
y = dsolve(eqn1,eqn2,eqn3);
y1=y.y1;
y2=y.y2;
y3=y.y3;
end
Paul on 6 Sep 2021
I was able to get Matlab to return an expression in terms of roots(), and I assumed that if a closed form for those roots existed Matlab would have provided it.

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