Could anyone help me with this warning please?

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This is my code :
function RunLogOscilNumeric3
k =10;
p0 =0.1;
t =(0:0.01:10000);
omega = 1;
N0 = 1;
[t,p]=ode23(@logOscilnumeric3,t,p0,[],omega,k,N0);
Pmax = max(p)
Pmean = mean(p)
figure(1)
plot(t,p)
title('The plot of the system with time')
xlabel ('Time')
ylabel ('The system' )
1;
% function dpdt = logOscilnumeric3(t,p,omega,k,N0)
% dpdt = N0*p - (N0*sin(omega*t)*p.^2/k);
% end
Notes: 1- Warning: Failure at t=5.060889e+00. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (1.421085e-14) at time t.
2- I tried to change the ode solver ,,but I still got this warning.
3- I want to solve this system for the specific values of the parameters and time'' I do not want to change those at all'' ,, because I am trying to solve different systems for the same parameters and time vector.
What should I do please?
Thanks in advance.

Accepted Answer

Torsten
Torsten on 5 Dec 2014
The analytical solution for your ODE is given by
p(t)=20*exp(t)/(exp(t)*(cos(t)-sin(t))-201)
This function has a singularity between t=5 and t=5.5.
Best wishes
Torsten.
  7 Comments
Avan Al-Saffar
Avan Al-Saffar on 28 Dec 2014
Dear Torsten If I have the following system : dx/dt = N0*sin(omega*t)*x - (N0*x.^2 / k)
I tried to solve it analytically but I am getting this formula which I can not continue:
( exp( (-N0/omega)*(cos(omega*t)) )/x)= ( integral( (N0/omega) * (exp( (-N0/omega) * (cos(omega*t)) )) )dt )
can you help me please?
Regards
Torsten
Torsten on 5 Jan 2015
Try MATLAB's dsolve.
If an explicit solution can not be found, you will have to solve the equation numerically for given values of N0, omega and k.
Best wishes
Torsten.

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