Answer:
Yes
Explanation:
Answer:
Yes, ode45 function can be used for solving 2nd order differential equations.
Explanation:
The ode45 function can be used to solve 2nd order differential equations if we convert the 2nd order differential equation into a system of first order differential equations.
Suppose we have the following 2nd order differential equation and we want to plot its solution for 0 ≤ t ≤ 10 with initial conditions y(0) = 2, and y'(0) = 1
d²y/dt² + 6dy/dt + 4y = -sin(3t)
make d²y/dt² subject of the equation
d²y/dt² = - 6dy/dt - 4y - sin(3t)
define variable x such that
dy/dt = x eq. 1
Now the above 2nd order differential equation can be written in terms of x as
dx/dt = -6x - 4y + sin(3t) eq. 2
in vector form
z = [x; y]
dz = [dx/dt; dy/dt]
where z and dz are column vectors
So we have successfully converted the 2nd order differential equation into two 1st order differential equations.
Now we have to translate it into a Matlab function.
Matlab Function:
function dz = func(t, z)
dz=[-6*z(1) -4*z(2) -sin(3*t); z(1)];
end
Where z(1) means x and z(2) means y
Save this function as func.m file in the Matlab directory.
Now we need driver code to call this function and plot its solution
Driver Code:
initial = [2; 1]; % given initial conditions of differential equation
range = [0 10]; % plot the solution in the range 0 ≤ t ≤ 10
[t, z]=ode45(@func,range,initial); % call 'func' in the ode45 function
plot(t, z(:,2)) % plot the results
grid on
Output:
Please refer to the attached image
