How to solve this system of ODEs?

I was try to study a dynamical system and for that after accounting for all factor I got the following system of differential equations:

[1]

and,

[2]

where c is a constant.

I want to find a solution to these differential equations. Is it possible to find an analytical or numerical solution of these equations using matlab. If so how?

I not very much familiar with the procedure for solving differential equations using matlab.

Thanks!

[James Tursa]

Do you have initial conditions for x, y, and dy/dt? If so, you could rewrite your equations as a system of three 1st order equations and use ode45( ) to find a numerical solution.

Answer 1

[Milan Padhiyar]

Hello Jaydev,

We can solve the coupled ODE system by using ‘ode45’ in MATLAB. This function requires arguments as first-order ODE equations, time, and initial conditions. By looking into your equation, the state vector of this system will be [x, y, y_dot], where y_dot is the derivative of y with respect to t.

So you need to rewrite both equations in a form of a column vector consisting of first-order ODEs. The LHS of column vector should look like [x_dot, y_dot, y_ddot], where x_dot and y_dot are derivative of x and y with respect to t respectively, and y_ddot is derivative of y with respect to t.

Please refer to the below link for the examples on ‘ode45’.

https://www.mathworks.com/help/matlab/ref/ode45.html

Thank You!