write a matlab code using dsolve to solve the ode y(t)''+ 2y'(t) + y(t) = 2 sin(t) + 6 cos(t) given y(0) = 2 and y'(0) = 0. in matlab

To solve the given ordinary differential equation (ODE) using dsolve in MATLAB, you can follow these steps:

1. Define the ODE equation as a function handle using @(t, y).
2. Set the initial conditions for y and y' using cond.
3. Solve the ODE using dsolve and store the symbolic solution.
4. Convert the symbolic solution to a function handle using matlabFunction.

Here is the MATLAB code:

main.m
% Step 1: Define the ODE equation
ode = @(t, y) diff(y, 2) + 2*diff(y) + y - 2*sin(t) - 6*cos(t);

% Step 2: Set initial conditions
y0 = 2;
yDot0 = 0;
conds = [y(0) == y0, diff(y)(0) == yDot0];

% Step 3: Solve the ODE
ySol(t) = dsolve(ode, conds);

% Step 4: Convert symbolic solution to function handle
ySolFun = matlabFunction(ySol(t));

% Test the solution
t = linspace(0, 10, 100);
y = ySolFun(t);

% Plot the solution
plot(t, y);
xlabel('t');
ylabel('y(t)');
title('Solution of the ODE');
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Make sure to replace y(0) and diff(y)(0) with appropriate syntax, as per the version of MATLAB you are using.

This code defines the ODE, sets the initial conditions, solves the ODE using dsolve, converts the symbolic solution to a function handle, and then tests and plots the solution.

Note: The solution may vary depending on the version of MATLAB you are using.