# How to solve coupled second order ODE?

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Juan Pedro Martinez on 26 Sep 2022
Answered: Torsten on 26 Sep 2022
Hello, I want to solve this system of equations (body falling with air resistance) to be able to blot x and y.
With initial conditions:
Does anyone have any pointers? Reading the documentation seems I need to write them as first order equations, but as I do not have de explicit function, I don't know how to obtain x and y.
Thank you!
##### 2 CommentsShowHide 1 older comment
Juan Pedro Martinez on 26 Sep 2022
Hello, thanks for your reply. You are right, I was jsut focusing on programming and forgot the math. I edited the question so the information is visible.

Torsten on 26 Sep 2022
b = 0.1;
fun = @(t,y)[y(2);-b*y(2)*sqrt(y(2)^2+y(4)^2);y(4);-b*y(4)*sqrt(y(2)^2+y(4)^2)];
y0 = [0;44.5;80;0];
tspan = [0,10];
[T,Y] = ode45(fun,tspan,y0);
plot(T,[Y(:,1),Y(:,3)])

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