solving a single differential equation by using ode45, but it can't solve should I write something else.

clc

ti = 0; %inital time

tf = 10E-5;% final time

tspan=[ti tf];

tc = 70E-9; %photon life time in cavity

P = 1; %pump strenght

k = 0.035; %critical coupling strength

l= 0.5;

s = 0.1;

f = @(t,y) [

- ((((s)^2).*k).*sin(y(1)-pi/2))./tc

];

%initial consitions

[T,Y] = ode45(f,tspan,[1]);

%plotting the graphs

plot(T,Y);

[Steven Lord]

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Answer 1

[Sam Chak]

@SAHIL SAHOO, based on the ODE in this image

the output probably becomes like this:

ti    = 0;      % inital time
tf    = 10E-5;  % final time
tspan = [ti tf];

% P = 1;  % pump strength (not used)
kappa = 0.035;  % critical coupling strength
L     = 0.5;
sigma = 0.1;
tauc  = 70E-9;  % photon life time in cavity

% differential equation
f = @(t,y) [- ((sigma^2)*kappa/tauc)*sin(y - pi/2) + L*(sigma^2)/(2*tauc)*sin(y + pi/2)/sqrt(1 + cos(y + pi/2))];

[T, Y] = ode45(f, tspan, 1);

plot(T, Y); grid on, xlabel('t'), ylabel({'$\varphi_{0}(t)$'}, 'Interpreter', 'latex')