MATLAB: Finding difficult to solve this coupled ode equations using ode45

help: finding difficult to solve this two coupled ode equations using ode45

I have been solving this two coupled ODE equations using ode45… Please find the attached files….
Even after defining the variable 'P'…,
I am getting an error
Undefined
function or
variable 'P'.
Error in
pair1 (line
5)
dy(1)=(P*(b^2)*v*sigma_e*((y(2)^2*sigma_e).^(-1/3))/(M^2))*exp(-Q/K*T)*sinh((sigma_e)/((M*K*T)*(b^3))*(Q/((y(2)).^2*sigma_e)).^(1/3));
Error in
@(t,y)pair1(t,y)
Error in
odearguments
(line 87)
f0 =
feval(ode,t0,y0,args{:});
% ODE15I sets
args{1} to
yp0.
Error in
ode45 (line
113)
[neq, tspan,
ntspan, next,
t0, tfinal,
tdir, y0, f0,
odeArgs,
odeFcn, …
Error in
ruban (line
13)
[t,y]=ode45(@(t,y)pair1(t,y),tspan,initial_conditions)
%function
call
Please help me to sort out this problem by modifying the code or providing the hints…
Any help will be appreciated

Best Answer

Parameterize your function as below:
 P=10E12;
 b=0.268E-9;
 Q=285;
 M=3;
 K=1.38E-23;
 v=3.6E16;
 sigma_e=200;
 T=923;
 ec=0.04;
 c=7; %provide your value
 tspan=0:0.01:70;
 initial_conditions=[0.01,100]; %change the intial condition according to your values
 [t,y]=ode45(@(t,y)pair1(t,y,P,Q,b,c,v,sigma_e,M,K,T,c,ec),tspan,initial_conditions)   %function call
 plot(t,y(:,1))
 
 
function dy=pair1(t,y,P,Q,b,c,v,sigma_e,M,K,T,c,ec)           %function definition
dy=zeros(2,1);
dy(1)=(P*(b^2)*v*sigma_e*((y(2)^2*sigma_e).^(-1/3))/(M^2))*exp(-Q/K*T)*sinh((sigma_e)/((M*K*T)*(b^3))*(Q/((y(2)).^2*sigma_e)).^(1/3));
dy(2)=(1/(y(2)*ec))*((c^2)-(y(2))^2)*y(1);
end
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