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# How to solve this system of ODEs?

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Jaydev Singh Rao on 25 Dec 2020
Answered: Milan Padhiyar on 28 Dec 2020
I was try to study a dynamical system and for that after accounting for all factor I got the following system of differential equations: and, 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!
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James Tursa on 26 Dec 2020
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.

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### Answers (1)

Milan Padhiyar on 28 Dec 2020
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’.
Thank You!
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