Stationary solution to differential equation

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SUMMARY

The discussion centers on finding the stationary solution to the differential equation 4(dy/dt) + 3y = sin(t) with the initial condition y(0) = 0. Participants clarify that the stationary amplitude is not derived directly from the particular solution y = sin(t)/3, as this does not represent a constant amplitude. Instead, the correct approach involves solving the homogeneous part of the equation and using the method of undetermined coefficients to find the particular solution in the form y = K cos(t) + M sin(t). The amplitude of the solution is determined by the coefficients K and M, which are derived from substituting back into the original equation.

PREREQUISITES
  • Understanding of ordinary differential equations (ODEs)
  • Familiarity with the method of undetermined coefficients
  • Knowledge of homogeneous and particular solutions
  • Basic trigonometric functions and their derivatives
NEXT STEPS
  • Study the method of undetermined coefficients in detail
  • Learn how to solve homogeneous differential equations
  • Practice finding particular solutions for inhomogeneous ODEs
  • Explore the concept of stationary solutions in differential equations
USEFUL FOR

Students and educators in mathematics, particularly those focused on differential equations, as well as anyone seeking to understand the behavior of solutions to inhomogeneous linear ODEs.

  • #31
I am more on this level of cherry picking:

http://tothevillagesquare.org/images/cherry-picking-numbers.jpg

I also regret to inform you that I have officially given up. This kind of problem is unlikely to show up on my exam tomorrow, and *if* one pops up, I can live with not completing it.
It won't ruin my A (or B or C or D for that matter).

I'm sorry to dissappoint you guys, after all your effort. Hopefully my teacher will cover this topic more thouroughly during the next semester. (which I've heard is almost a dedicated differential equation semester)
 
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  • #32
Aaaah, you like 'em big! :smile:

Will you let us know how your exam went?
(And if something like this popped up?)
 
  • #33
Of course :)

(and btw, sorry about the huge dimmensions )
 
  • #34
It went very well for my exam, and luckily no differential equations containing those spooky sine functions :)

After studying the solution which was published earlier this evening, I feel like I'm in the right spot for an A :)
 
  • #35
Good! :smile:

And I guess we'll get back to DE's later. ;)
 

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