Solving an ODE with ode45 on [0,10]

[nashat]

Homework Statement

solve the initial problem using ode45 on the interval [0,10]

Homework Equations

cost dy/dt + ysint = 2t cos^2(t) y(0) = -Pi

The Attempt at a Solution

I have no I dia how to sart

 

[wildman]

Matlab has an excellent help page. Press the help button on the tool bar and when the help page comes up, go to search and enter ode45. You can also do a google seach for ode45, usually that comes up with a lot of examples. Check out the ones with .edu. Those are usually the best. Once you have read that and it is still not working for you, then come here and ask a more specific question.

 

[piercas]

this problem.

it is important to approach problems with a systematic and logical mindset. In order to solve this ODE using ode45 on the interval [0,10], we need to first understand the problem and what is being asked. The given equation is a first-order differential equation with an initial condition. This means that we need to find the solution y(t) that satisfies the equation and the given initial condition.

To start, we can rewrite the equation in a more familiar form:

dy/dt = (2t cos^2(t) - ysint) / cos(t)

Now, we can use ode45, which is a numerical method for solving differential equations, to find the solution. The syntax for using ode45 is:

[t,y] = ode45(@function, [t0,tf], y0)

Where @function is the name of the function that represents the ODE, [t0,tf] is the interval over which we want to solve the ODE, and y0 is the initial condition. In this case, our function would be:

function dydt = ode_function(t,y)
dydt = (2*t*cos(t)^2 - y*sin(t)) / cos(t);

Now, we can input this into ode45 to solve the ODE:

[t,y] = ode45(@ode_function, [0,10], -pi);

The output will be an array of values for t and y, which represent the solution to the ODE on the interval [0,10]. We can plot this solution and see how it behaves over time.

In summary, to solve this ODE using ode45 on the interval [0,10], we first need to understand the problem and rewrite the equation in a familiar form. Then, we can use the syntax for ode45 to find the solution and plot it to see the behavior over time. This method can be applied to solve many other ODEs as well.