Solving Coupled second order differential equations

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SUMMARY

This discussion focuses on the approach to solving coupled second-order differential equations, specifically addressing whether the order of solving these equations impacts the solution time. Participants noted that while they typically solve the first equation, they have not observed significant differences in ease or efficiency. An example provided includes the equations dy/dt = y and dx/dt = y + 3x, highlighting the nature of coupling in differential equations.

PREREQUISITES
  • Understanding of second-order differential equations
  • Familiarity with coupled differential equations
  • Knowledge of auxiliary equations and their roots
  • Basic differential calculus
NEXT STEPS
  • Study methods for solving coupled second-order differential equations
  • Explore the implications of solving order on solution efficiency
  • Learn about the role of auxiliary equations in coupled systems
  • Investigate numerical methods for solving differential equations
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Students and professionals in mathematics, engineering, and physics who are working with differential equations, particularly those dealing with coupled systems and seeking to optimize their solving strategies.

SpartanG345
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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?
 
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SpartanG345 said:
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?
 
say dy/dt = y
and dx/dt = y + 3x

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

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