Solving 3 simultaneous first order differential equations

I need to solve the following set of differential equations using MATLAB.

Here, um,Ks,Kp,a,sm,yxs,K1,K2-constant values s,p,x- variables

I am using the function ode45 for this. This is my program :

function dydt=react(t,y)
dydt=zeros(3,1);
um=0.71;
ks=37.72;
sm=510;
kp=160.83;
a=0.81;
yxs=0.03;
ms=0.0011;
k1=33.04;
k2=0.0001;

y=zeros(3,1);
x=y(1);
s=y(2);
p=y(3);

dx=(um*(s/(s+ks))*((1-(s/sm))^a)*(kp/(kp+p)))*x;
ds=-1*((um/yxs)*(s/(s+ks))*((1-(s/sm))^a)*(kp/(kp+p)) + ms)*x;
dp=(k1*(um*(s/(s+ks))*((1-(s/sm))^a)*(kp/(kp+p)))+k2)*x;
dydt=[dx;ds;dp];

On giving this command :

[T,Y]=ode45('react',[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[0.2 100 0.2]);

or this command :

[T,Y]=ode45('react',[0 15],[0.2 100 0.2]);

All I get is this :

Y =

0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000

i.e the equations are not being solved. I am just getting the initial values of my inputs (i.e x,s,p) as the output.

Any help is appreciated.

[Walter Roberson]

Should be merged with duplicate http://www.mathworks.co.uk/matlabcentral/answers/110772-solving-3-simultaneous-first-order-differential-equations

Answer 1

[Azzi Abdelmalek]

Because in react function you added

y=zeros(3,1);

Remove this line

[Abhivyakti]

Thankyou soo much! That worked.

Another doubt I have. I need to plot the graphs of 'dx/dt vs t', 'ds/dt vs t' and 'dp/dt vs t'.

I cannot figure out how to get an equation between 'dx/dt and t' , i.e how to consider the variation of 'dx/dt' with 't' in one equation as 'dx/dt varies as the variation of 's' & 'p' wrt 't'.

[Abhivyakti]

Basically , I think if I have the equation of each 'x' with respect to 't', I can differentiate that & obtain 'dx/dt'. So, can I get the equation of 'x' wrt 't' ( as its obtained using function dsolve) by using 'ode23 or ode45' ????