Decoupling Differential Equations: Can Substitution Simplify the System?

[delve]

$$\ddot{x}=\dot{z}$$

$$\ddot{z}=\dot{x}$$

there should be z with a dot above it just like the x, but there is none, and the code is correct as far as I know. Can someone help? Thanks.

 

[hamster143]

Coupled.

 

[delve]

do you know what makes it coupled?

 

[hamster143]

The fact that there are no equations that contain only x or only z.

 

[delve]

Thank you :)

 

[hamster143]

Also notice that if you use a substitution u=x+z, v=x-z, you get a pair of uncoupled equations.