Using ode to solve a specific differential equation

I need help solving this specific differential equation using ode45 in MATLAB. The differential equation is k*(dT/dt)= A*Q*(1-b(T)) - S*c*E*(T^4). We have all of the values but I need code to solve and plot different solutions to the ode.

[William Rose]

@Allison Reynolds, what have you done so far? When you say you need to solve and plot different solutions, what do you mean? Different initial conditions? Different values for the constants?

Please post what you have done so far, including values for the initial conditions and the constants.

[William Rose]

@Allison Reynolds, does Q(1-b(T)) mean Q*(1-b*T))? If not, then specify what the functions b and Q are.

Answer 1

[Star Strider]

Try these —

% k*(dT/dt)= A*Q(1-b(T)) - S*c*E*(T^4)

odefcn = @(t,T,a,b,c,E,k,Q,S) (a*Q*(1-b*T) - S*c*E*(T^4))/k;                % If 'Q' Is A Scalar

a = rand;
b = rand;
c = rand;
E = rand;
k = rand;
Q = rand;
S = rand;
tspan = [0 20];
ic = 0.42;
[t,T] = ode45(@(t,T)odefcn(t,T,a,b,c,E,k,Q,S), tspan, ic);

figure
plot(t,T)
grid

odefcn = @(t,T,a,b,c,E,k,Q,S) (a*Q(1-b*T) - S*c*E*(T^4))/k;                 % If 'Q' Is A Function

a = rand;
b = rand;
c = rand;
E = rand;
k = rand;
S = rand;
Q = @(x) sin(x) .* cos(x);                                                  % Make Something Up
tspan = [0 20];
ic = 0.42;
[t,T] = ode45(@(t,T)odefcn(t,T,a,b,c,E,k,Q,S), tspan, ic);

figure
plot(t,T)
grid

Experiment to get the desired result.

.

[William Rose]

Nice compact and elegant solution by @Star Strider

[Star Strider]

Thank you!