usage of ode45

i have 3 differential eqns that i would like to solve using ode45. M, l1, V are all varying w.r.t. time evrything else are just constants

Answer 1

[Star Strider]

imshow(imread('WhatsApp Image...16.45 PM.jpeg'))

syms M(t) I_1(t) I_2 V(t) t g mu A Y T
Eq1 = diff(M) == -g*V*A

Eq1(t) = 

Eq2 = diff(V) == I_1*g/(I_1+I_2) - 8*pi*mu*V/(g*A)

Eq2(t) = 

Eq3 = diff(I_1) == -V

Eq3(t) = 

[VF,Subs] = odeToVectorField(Eq1, Eq2, Eq3)

VF = 

Subs = 

fcn = matlabFunction(VF, 'Vars',{T,Y,g,I_2,mu,A})

fcn = function_handle with value:
    @(T,Y,g,I_2,mu,A)[(g.*Y(3))./(I_2+Y(3))-(mu.*pi.*Y(1).*8.0)./(A.*g);-A.*g.*Y(1);-Y(1)]

g = rand

g = 0.3866

I2 = rand

I2 = 0.7057

mu = rand

mu = 0.0208

A = rand

A = 0.1406

[t,y] = ode45(@(t,y)fcn(t,y,g,I2,mu,A), [0,100], rand(3,1));

figure
plot(t, y)
grid
xlabel('Time')
ylabel('Amplitude')
legend(string(Subs), 'Location','best')

Make appropriate corrections to the symbolic variables (I am not certain that I transcribed them correctly), supply values for the constants parameters, and then use ode45 (or ode15s if the parameters vary significantly in magnitude) to solve it numerically.

.

[Hicham]

what was the function matlabFunction that u used. and how can i program it without the usage of the first ode dm/dt

[Star Strider]

The matlabFunction function is part of the Symbolic Math Toolbox.

If you do not want to include the first differential equation, do not include it in the odeToVectorField arguments, using:

[VF,Subs] = odeToVectorField(Eq2, Eq3)

instead.

.