Stationary solution to differential equation

Click For Summary

Homework Help Overview

The discussion revolves around finding the stationary amplitude of a sine wave described by the differential equation 4 \frac{dy}{dt} + 3y = sin(t) with the initial condition y(0) = 0. Participants are exploring the concept of stationary solutions in the context of differential equations.

Discussion Character

  • Conceptual clarification, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the definition of stationary solutions and whether the stationary amplitude can be derived from the particular solution. There is confusion about the relationship between stationary solutions and the particular solution, particularly in the context of sine functions.

Discussion Status

The discussion is active, with participants questioning their understanding of stationary solutions and the method of undetermined coefficients. Some have suggested that the amplitude of the sine function is not constant, leading to further exploration of the correct approach to finding the particular solution.

Contextual Notes

Participants express uncertainty regarding the application of previous knowledge from other exercises involving constant results, indicating a potential misunderstanding of how sine functions affect the stationary solution in this context.

  • #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)
 
Last edited by a moderator:
Physics news on Phys.org
  • #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. ;)
 

Similar threads

Determine whether ## S[y] ## has a maximum or a minimum
  • · Replies 18 ·
Replies
18
Views
3K
How do we write a sinusoidal solution to a 2nd order DE as a sum of exponentials raised to complex roots?
  • · Replies 2 ·
Replies
2
Views
3K
What is a Different Method for Implicit Differentiation?
  • · Replies 2 ·
Replies
2
Views
2K
Finding the rate of change of x in the equation
  • · Replies 8 ·
Replies
8
Views
2K
Relationship between autonomous system and related single equation
  • · Replies 3 ·
Replies
3
Views
2K
How should I find the equilibrium points and the general equation?
  • · Replies 3 ·
Replies
3
Views
2K
Question on Two Differentiation Techniques
  • · Replies 25 ·
Replies
25
Views
2K
Discontinuous partial derivatives example
  • · Replies 2 ·
Replies
2
Views
2K
Given unit impulse response, obtain differential equation
  • · Replies 7 ·
Replies
7
Views
2K
Obtain a nonzero solution of ##y''-4y'+x^2(y'-4y)=0## by inspection
  • · Replies 7 ·
Replies
7
Views
2K