Solving Coupled second order differential equations

[SpartanG345]

Just wondering does it matter which coupled differential equation you solve first
( i terms of time)?

normally i just solve the first equation, so far all our tutorial question involved finding solutions to second order equations that have 2 distinct roots ( for the auxilliary equation)

I normally rend to solve the more simpler coupled equation, but so far there has not been a difference in ease.

anyone have any tips?

[HallsofIvy]

Just wondering does it matter which coupled differential equation you solve first
( i terms of time)?

normally i just solve the first equation, so far all our tutorial question involved finding solutions to second order equations that have 2 distinct roots ( for the auxilliary equation)

I normally rend to solve the more simpler coupled equation, but so far there has not been a difference in ease.

anyone have any tips?
If the equations are coupled, how can you "just solve the first equation" without regard to the second equation? I don't understand what you are saying. Can you give an example?

[SpartanG345]

say dy/dt = y
and dx/dt = y + 3x

i thought those equation were coupled, while the 1st one can be solved independently