Here it is:

```matlab

% Define the differential equation and boundary conditions

function dydt = ode9(t, y, p)

% Parameters

p1 = p(1); p2 = p(2); p3 = p(3);

% Differential equation

dydt = [

y(2);

y(3);

y(4);

y(5);

y(6);

y(7);

y(8);

y(9);

-p1*y(1) - p2*y(2) - p3*y(3)

];

end

% Boundary conditions

function bc = bc9(ya, yb, p)

% Parameters

p1 = p(1); p2 = p(2); p3 = p(3);

% Boundary conditions

bc = [

ya(1) - 0; % Velocity at x = 0

ya(2) - 1; % Velocity gradient at x = 0

ya(3) - 2; % Temperature at x = 0

ya(4) - 3; % Temperature gradient at x = 0

ya(5) - 4; % Concentration at x = 0

ya(6) - 5; % Concentration gradient at x = 0

yb(1) - 6; % Velocity at x = L

yb(2) - 7; % Velocity gradient at x = L

yb(3) - 8 % Temperature at x = L

];

end

% Shooting method

function [y, p] = shoot9(p0, tspan, y0)

% Initial guess for parameters

p = p0;

% Solve the differential equation

[t, y] = ode45(@(t,y) ode9(t, y, p), tspan, y0);

% Evaluate the boundary conditions

bc = bc9(y(1,:), y(end,:), p);

% Update the parameters using the Newton-Raphson method

while norm(bc) > 1e-6

J = jacobian(@(p) bc9(y(1,:), y(end,:), p), p);

dp = -J\bc;

p = p + dp;

[t, y] = ode45(@(t,y) ode9(t, y, p), tspan, y0);

bc = bc9(y(1,:), y(end,:), p);

end

end

% Example usage

tspan = [0 1];

y0 = [0 1 2 3 4 5 0 0 0];

p0 = [1 2 3];

[y, p] = shoot9(p0, tspan, y0);

```

the `ode9` function defines the 9th order differential equation, and the `bc9` function defines the 9 boundary conditions (velocity, temperature, and concentration at the start and end of the domain). The `shoot9` function implements the shooting method to solve the problem.

The shooting method involves guessing the initial parameter values (`p0`), solving the differential equation, evaluating the boundary conditions, and then updating the parameters using the Newton-Raphson method until the boundary conditions are satisfied within a specified tolerance.

Hope it helps!

partial credit AI tools

It's maybe your answer:It's maybe your answer:

MATLAB CODES:

function shooting_method

% Define the boundary conditions

bc = [bc1, bc2, bc3, bc4, bc5, bc6, bc7, bc8, bc9];

% Initial guess for the unknown initial conditions

init_guess = [guess1, guess2, guess3, guess4, guess5, guess6, guess7, guess8, guess9];

% Options for ode45

options = odeset('RelTol',1e-8, 'AbsTol',1e-10);

% Solve using fsolve to adjust the initial conditions

sol = fsolve(@(init_cond) boundary_conditions(init_cond, bc, options), init_guess);

% Final solution with correct initial conditions

[t, y] = ode45(@differential_eq, [t0 tf], sol, options);

% Plot the results

plot_results(t, y);

end

function dydt = differential_eq(t, y)

% Define the 9th order differential equation as a system of first-order ODEs

dydt = zeros(9,1);

% dydt(1) = y2, dydt(2) = y3, ..., dydt(9) = f(y1, y2, ..., y9)

dydt(1) = y(2);

dydt(2) = y(3);

% ...

dydt(9) = ...; % Define the actual 9th order differential equation

end

function res = boundary_conditions(init_cond, bc, options)

% Integrate the differential equation with the current initial conditions

[t, y] = ode45(@differential_eq, [t0 tf], init_cond, options);

% Calculate the residuals at the boundary

res = zeros(9,1);

res(1) = y(end, 1) - bc(1); % Boundary condition for y1 at t = tf

res(2) = y(end, 2) - bc(2); % Boundary condition for y2 at t = tf

% ...

res(9) = y(end, 9) - bc(9); % Boundary condition for y9 at t = tf

end

function plot_results(t, y)

% Plot the results

figure;

plot(t, y(:, 1), 'DisplayName', 'y1');

hold on;

plot(t, y(:, 2), 'DisplayName', 'y2');

% ...

plot(t, y(:, 9), 'DisplayName', 'y9');

hold off;

legend show;

xlabel('Time');

ylabel('Solution');

title('Solution of 9th Order Differential Equation using Shooting Method');

end