Guessing the particular solution

In summary, the conversation is about finding both a particular solution and a general solution for the equation y(2)-6y(1)=25sin(6x). The author suggests a particular solution of yp(x)=Asin(6x) and takes derivatives to simplify the equation. They then realize they need to include cosine terms as well and thank the responder for their suggestion.
  • #1
jdawg
367
2

Homework Statement


Find both a particular solution yp (via the method of educated guess) and a general solution y.
y(2)-6y(1)=25sin(6x)

Homework Equations

The Attempt at a Solution


This was my guess:
yp(x)=Asin(6x)
I then took derivatives, plugged them in, and simplified to get this:
-27Asin(6x)-36Acos(6x)=25sin(6x)
I'm stuck at this point! How do I solve for A? Or did I just make a bad guess for the particular solution?
 
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  • #2
you end up with sin and cos terms, so it makes sense to try as particular solution also something with sin and cos terms:
[itex]y_p = A\sin(6x) + B\cos(6x)[/itex]
 
  • Like
Likes jdawg
  • #3
Ohhhh duh, thanks so much!
 

1. What is "guessing the particular solution"?

"Guessing the particular solution" is a method used in science to find a specific solution to a problem or equation. It involves making an educated guess or estimation based on available information and testing the guess to see if it is correct.

2. When is "guessing the particular solution" used?

"Guessing the particular solution" is often used when there is limited or incomplete information available to solve a problem or equation. It can also be used as a starting point for more complex problem-solving methods.

3. How accurate is "guessing the particular solution"?

The accuracy of "guessing the particular solution" depends on the quality of the initial guess and the amount of testing and refinement that is done. It is not always a precise method, but it can provide a useful starting point for further investigation.

4. What are the advantages of "guessing the particular solution"?

One advantage of "guessing the particular solution" is that it can be a quick and simple way to find a solution to a problem. It also allows for creativity and outside-the-box thinking, which can lead to unexpected and innovative solutions.

5. Are there any limitations to "guessing the particular solution"?

Yes, there are limitations to "guessing the particular solution." It may not always provide an accurate or precise solution, and it may not work for all types of problems or equations. It is important to test and refine the initial guess to improve its accuracy.

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