MATLAB: Find difficult in solving these four coupled ODE’s using ODE45….I have attached a file regarding these equations..

Question

function dy=pair(t,y,a,b,d,hstress,sigma,Hstar,kc,c) 
dy(1)=  a*sinh((b*(sigma^d)*(1-y(2)))/((1-y(3))*(1-y(4)))) ;
dy(2)=((hstress*(a*sinh(b*(sigma^d)*(1-y(2)))/(1-y(3))*(1-y(4))))/(sigma^d))*(1-y(2)/Hstar);
dy(3)=(kc/3)*power((1-y(3)),4);
dy(4)=  c*y(1);
dy=dy';
end
Error
>> a=0.5179;
>> b=1.1003E-3;
>> c=0.4576;
>> d=1;
>> hstress=3463.46;
>> Hstar=0.7846;
>> Kc=0.1137;
>> tspan=0:0.01:40;
 pair
Error using pair (line 3)
Not enough input arguments.
 
>> pair
Error using pair (line 3)
Not enough input arguments.
 
>> [t,y]=ode45(@pair,tspan,[0 0 0 0 0]);

I suspect I know a bit of what's going wrong, yet I'm at a loss for how to fix it. Any help is much appreciated!

Answer 1

 a=0.5179;
 b=1.1003E-3;
 c=0.4576;
 d=1;
 hstress=3463.46;
 Hstar=0.7846;
 Kc=0.1137;
 tspan=0:0.01:40;
 initial_conditions=[0;0;0;0]  %change the intial condition according to your values
 [t,y]=ode45(@(t,y)pair(t,y,a,b,d,hstress,sigma,Hstar,Kc,c),tspan,initial_conditions)   %function call
 plot(t,y(:,1))
 
function dy=pair(t,y,a,b,d,hstress,sigma,Hstar,kc,c)           %function definition
dy=zeros(4,1);
dy(1)=a*sinh((b*(sigma^d)*(1-y(2)))/((1-y(3))*(1-y(4)))) ;
dy(2)=((hstress*(a*sinh(b*(sigma^d)*(1-y(2)))/(1-y(3))*(1-y(4))))/(sigma^d))*(1-y(2)/Hstar);
dy(3)=(kc/3)*power((1-y(3)),4);
dy(4)=c*y(1);
end