solving a coupled system of differential equations

Hello everyone,

I have two differential equations which are coupled. I tried to use ode45 but it doesn't work because the system is coupled.

Any suggestions on how to solve this system ?

Here is my system:

x_double_dot + z_double_dot = 2*x_dot*z_dot

z_double dot + 3*x_double_dot=-3*x*z

Thank you in advance !

Answer 1

[Torsten]

Can you solve

a   + b = 2*x_dot*z_dot
3*a + b = -3*x*z

for a and b ?

Once you've done this, your system can be written as

x_double_dot = f1(x,z,x_dot,z_dot)
z_double_dot = f2(x,z,x_dot,z_dot)

Now transform this system to a first-order system as explained in the example "Solve Nonstiff Equation" under

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

[nado]

Thank u @Torsten