How to Solve a system of first order differential equation in MATLAB?

how to write the command to solve series of differential equation in MATLAB

Dx/Dt = (a+b+c)*x + k*y + l*z

Dy/Dt = k*y + a*x

Dz/Dt = l*z + b*x

[dawar]

S = S + c(i)*x^(i-1) find the first order ordinary differential equation

Answer 1

[Vaclav Ondra]

Have a look at examples on ode solvers page. There's an example of the system of ODEs. Simply rewrite your system into Matlab form, i.e.

function dydt = f(t,y)
dydt = [(a+b+c)y(1) + k*y(2) + I*y(3)
 k*y(2) + a*y(1)
 I*y(3) + b*y(1)];
end

and use, for example, ode45 solver

tspan = [0 1]; % your time interval
y0 = [1; 0; 0]; % your initial conditions
[t,y] = ode45(@f,tspan,y0); % solver

Everything is explained in the documentation.

[Le Duc Long]

Hi Vaclav Ondra.

Can you show me code to solve system of non-homogeneous first order differential equation in MATLAB?

Or where can i see method.

Thanks so much.

Best regards!

[Muhammad Sinan]

You can program this problem is a single script file such as

%% Parameter
a = ?;
b = ?;
c = ?;
k = ?;
I = ?;
%% Initial Conditions
IC = [?, ?, ?];
%% Time span
tinitial = ?;
tfinal = ?;
df = ?;
t = linspace(tinitial, tfinal, df);
%% Model/ system of differential equations
Model = @(t, X) [(a+b+c)*X(1) + k*X(2) + l*(3);
    k*X(2) + a*X(1);
    l*X(3) + b*X(1)];
%% Solution
sol = ode45(Model, t, IC);
sol = deval(sol, t)
%% Substituitions for the dependent variables
x = X(1);
y = X(2);
z = X(3);

%% Plot by a single figure
plot(t, sol)
legend("x", "y", "z")

%% Plot separately
figure(1)
plot(t, x)
xlabel("Time")
ylabel("Solution of Dx/Dt")

figure(2)
plot(t, y)
xlabel("Time")
ylabel("Solution of Dy/Dt")

figure(3)
plot(t, z)
xlabel("Time")
ylabel("Solution of Dz/Dt")

Please replace the "?" by your desired syntex.

[omar A.alghafoor]

there is error in

%% Substituitions for the dependent variables

x = X(1);

y = X(2);

z = X(3);

Undefined function 'X' for input arguments of type 'double'.

Error in solve_ode45_test (line 201)

x = X(1);

why ???

Answer 2

[Nur]

syms y(x)
ode (x) =diff (y(x),x) == (2*((y(x))^2 + X^2)) / (y(x)*x);

ode(x) =

Invalid expression. Check for missing or extra characters.

Error in connector.internal.fevalMatlab

Error in connector.internal.fevalJSON

diff(y(x),x) == (2*y(x)^2) + 2*X^2)/(x*y(x))

cond = y(2) == -1;
 ySol(x) = dsolve (ode , cond)

ySol(x) =

-(x^4*(X^2/16 + 1/16) - X^2)^(1/2)