% Define initial parameters
lambda_init = 2;
kappa_init = 1;
theta_k_init = pi/10;
R_init = 7;
rout = 3;

% Define c
c = sqrt(4 – (rout/R_init)^2);

% Define the function for the differential equations
f = @(r, y) [y(2); ((-1*(lambda_init+1)*(r*y(2)+y(1)))+(1/r)*((kappa_init*r^2*cos(theta_k_init)-(lambda_init+1))*y(1))-(kappa_init*r*y(3)*sin(theta_k_init))+(-16*lambda_init*r^2)/(c^4*R_init^2)); y(4); ((-1*(r*y(4)+y(3)))+(1/r)*((kappa_init*r^2*cos(theta_k_init)-1)*y(3))+(kappa_init*r*y(1)*sin(theta_k_init)))];

% Solve the differential equations using ode45
r_span = linspace(0, rout, 100); % Define the range of r values
[~, sol] = ode45(f, r_span, [0, 0, 0, 0]);

% Extract solutions
dr_sol = sol(:,1);
dtheta_sol = sol(:,3);

% Plot the solutions
figure;
subplot(2,1,1);
plot(r_span, dr_sol, ‘b-‘);
xlabel(‘r’);
ylabel(‘dr(r)’);
title(‘Solution of dr(r) vs r’);

subplot(2,1,2);
plot(r_span, dtheta_sol, ‘b-‘);
xlabel(‘r’);
ylabel(‘dtheta(r)’);
title(‘Solution of dtheta(r) vs r’);

I am trying to solve the coupled differential eqns for d_r(r) vs r and d_theta(r) vs r for these parameter values and boundary conditions so that it is zero at both end d_r(0) = d_r(rout) = 0 and the same for d_theta. However, Not able to see the plot and data. please suggest me errors.% Define initial parameters
lambda_init = 2;
kappa_init = 1;
theta_k_init = pi/10;
R_init = 7;
rout = 3;

% Define c
c = sqrt(4 – (rout/R_init)^2);

% Define the function for the differential equations
f = @(r, y) [y(2); ((-1*(lambda_init+1)*(r*y(2)+y(1)))+(1/r)*((kappa_init*r^2*cos(theta_k_init)-(lambda_init+1))*y(1))-(kappa_init*r*y(3)*sin(theta_k_init))+(-16*lambda_init*r^2)/(c^4*R_init^2)); y(4); ((-1*(r*y(4)+y(3)))+(1/r)*((kappa_init*r^2*cos(theta_k_init)-1)*y(3))+(kappa_init*r*y(1)*sin(theta_k_init)))];

% Solve the differential equations using ode45
r_span = linspace(0, rout, 100); % Define the range of r values
[~, sol] = ode45(f, r_span, [0, 0, 0, 0]);

% Extract solutions
dr_sol = sol(:,1);
dtheta_sol = sol(:,3);

% Plot the solutions
figure;
subplot(2,1,1);
plot(r_span, dr_sol, ‘b-‘);
xlabel(‘r’);
ylabel(‘dr(r)’);
title(‘Solution of dr(r) vs r’);

subplot(2,1,2);
plot(r_span, dtheta_sol, ‘b-‘);
xlabel(‘r’);
ylabel(‘dtheta(r)’);
title(‘Solution of dtheta(r) vs r’);

I am trying to solve the coupled differential eqns for d_r(r) vs r and d_theta(r) vs r for these parameter values and boundary conditions so that it is zero at both end d_r(0) = d_r(rout) = 0 and the same for d_theta. However, Not able to see the plot and data. please suggest me errors. % Define initial parameters
lambda_init = 2;
kappa_init = 1;
theta_k_init = pi/10;
R_init = 7;
rout = 3;

% Define c
c = sqrt(4 – (rout/R_init)^2);

% Define the function for the differential equations
f = @(r, y) [y(2); ((-1*(lambda_init+1)*(r*y(2)+y(1)))+(1/r)*((kappa_init*r^2*cos(theta_k_init)-(lambda_init+1))*y(1))-(kappa_init*r*y(3)*sin(theta_k_init))+(-16*lambda_init*r^2)/(c^4*R_init^2)); y(4); ((-1*(r*y(4)+y(3)))+(1/r)*((kappa_init*r^2*cos(theta_k_init)-1)*y(3))+(kappa_init*r*y(1)*sin(theta_k_init)))];

% Solve the differential equations using ode45
r_span = linspace(0, rout, 100); % Define the range of r values
[~, sol] = ode45(f, r_span, [0, 0, 0, 0]);

% Extract solutions
dr_sol = sol(:,1);
dtheta_sol = sol(:,3);

% Plot the solutions
figure;
subplot(2,1,1);
plot(r_span, dr_sol, ‘b-‘);
xlabel(‘r’);
ylabel(‘dr(r)’);
title(‘Solution of dr(r) vs r’);

subplot(2,1,2);
plot(r_span, dtheta_sol, ‘b-‘);
xlabel(‘r’);
ylabel(‘dtheta(r)’);
title(‘Solution of dtheta(r) vs r’);

I am trying to solve the coupled differential eqns for d_r(r) vs r and d_theta(r) vs r for these parameter values and boundary conditions so that it is zero at both end d_r(0) = d_r(rout) = 0 and the same for d_theta. However, Not able to see the plot and data. please suggest me errors. eqn solve, plotting MATLAB Answers — New Questions

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