dsolve error (simultaneous differential equations)

clear all
close
clc

m = 10;
k = 1000;
u0 = 0.01;

syms y1 y2

f=dsolve('m*D2y1+2*k*y1-k*y2==0,m*D2y2-k*y1+2k*y2==0','y1(0)==0,Dy1(0)==0,Dy2(0)==0,y2(0)==0.01');

figure
ezplot(f,[0 100]);

I want to solve simultaneous differential equation but i have a problem solving it.

Can someone help me find whats causing error?

Answer 1

[Sulaymon Eshkabilov]

Here is the answer:

clear all
close
clc
m = 10;
k = 1000;
u0 = 0.01;
syms y1(t) y2(t)
Dy1=diff(y1);
Dy2=diff(y2);
D2y1=diff(y1, 2);
D2y2=diff(y2, 2);
Eqn1=m*D2y1+2*k*y1-k*y2;
Eqn2=m*D2y2-k*y1+2*k*y2;
ICs=[y1(0)==0,Dy1(0)==0,Dy2(0)==0,y2(0)==0.01];
f=dsolve(Eqn1,Eqn2, ICs);
figure
ezplot(f.y1,[0 100]), hold on
ezplot(f.y2, [0, 100]), legend('y_1(t)', 'y_2(t)', 'location', 'best')

[Seungwon Lee]

Thanks for the Answer.

Can you tell me when i should define differential equation as

Dy1=diff(y1);
Dy2=diff(y2);
D2y1=diff(y1, 2);
D2y2=diff(y2, 2);

as you mentioned?

Because sometimes it works eventhough i don't define like that.

[Sulaymon Eshkabilov]

There two different ways of expressing ODE expressions. This is one of them and is the logically structured one. The other one is direct that you define your variable without specifying to differentuiate it w.r.t what variable that may create a problem in cases when there is an obscurity with the existing variables in your MATLAB workspace.

Good luck

[Seungwon Lee]

Thanks