solving equation using ode45 in matlab

Question

I have this equation B1*(phi) + B2*(d(phi)/ds) -B3(d^2(phi)/ds^2) = 0. here B1, B2, B3 are 4D matrices. the initial condition are phi = 0 at s = 0 and d(phi)/ds = 0 at s = 0.

% Define the anonymous function for the equation
equation = @(s, phi_dphi) [phi_dphi(2); -B1.*phi_dphi(1) + B2.*phi_dphi(2) - B3.*(phi_dphi(2).^2)];

% Define the initial conditions
phi0 = [0;0;0;0]; % Initial condition for phi
dphi_ds0 = [0;0;0;0]; % Initial condition for d(phi)/ds

% Set the options for ode45 (optional)
options = odeset('RelTol', 1e-6, 'AbsTol', 1e-6);

% Solve the equation using ode45
[t, phi_dphi] = ode45(equation, [S_0, S_L], [phi0; dphi_ds0], options);

% Extract the solution for phi and d(phi)/ds
phi = phi_dphi(:, 1);
dphi_ds = phi_dphi(:, 2);

% Display the results
disp('Solution:')
disp('---------')
disp('s phi d(phi)/ds')
disp([t, phi, dphi_ds]);