Diff eq: I dont understand my prof's comments. Here is my work.

In summary, the conversation discusses a student's incorrect answer on an exam and the professor's comments on their work. The student asks about the general solution, fundamental set, and yp, and the professor clarifies that the student should have started with the differential equation to find the general solution rather than substituting. The professor also points out that the student did not identify yp or show that each of their solutions are particular solutions to the homogeneous equation. The student acknowledges the mistake and asks for confirmation on their revised approach.
  • #1
frozenguy
192
0
So I had an exam and got this problem wrong, that I had done incorrectly on the quiz as well. comments in red under picture are comments from professor.

here is the work:
prob1text.jpg


Attempt)
prob1attempt.jpg

Why is this general solution? What is the fundamental set? What is yp? (this should be verified)

So on the exam, in addition to what I did, I should of found the first, second, and third derivatives of each y1,2,3 and then separately substitute them into the non homogeneous eqn to check for validity?

And uh, WOW. I could of sworn I wrote out yp.. So if write yp=2x-12x2ex that would satisfy that part right?
 
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  • #2
I think your professor wanted you to start with the differential equation and work to get the general solution rather than substituting the equation they gave you into the DE.
 
  • #3
You found y1, y2 and y3, but did not identify yp.

You showed that y1, y2 and y3 are linearly independent, but you did not show that each one is a particular solution to the homogeneous equation.

Finally, you should have shown that yp is the particular solution to the non-homogeneous equation.
 
  • #4
rock.freak667 said:
I think your professor wanted you to start with the differential equation and work to get the general solution rather than substituting the equation they gave you into the DE.
Ok thanks!

Dickfore said:
1.)You found y1, y2 and y3, but did not identify yp.

2.)You showed that y1, y2 and y3 are linearly independent, but you did not show that each one is a particular solution to the homogeneous equation.

3.)Finally, you should have shown that yp is the particular solution to the non-homogeneous equation.
So maybe like this?
prob1correction.jpg
 

Related to Diff eq: I dont understand my prof's comments. Here is my work.

1. What is a differential equation?

A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It is commonly used in many scientific disciplines to model various phenomena, such as growth, motion, and changes in physical systems.

2. Why is understanding my professor's comments important?

Understanding your professor's comments is important because it allows you to improve your work and deepen your understanding of the subject. Your professor's comments can also provide valuable insights and feedback on your thought process and problem-solving skills.

3. How do I interpret my professor's comments?

Interpreting your professor's comments involves carefully reading and analyzing what they have written. Look for specific areas where they have provided feedback or suggestions for improvement. You can also ask your professor for clarification if you are unsure about their comments.

4. What should I do if I still don't understand my professor's comments?

If you are still having trouble understanding your professor's comments, you can ask for help from your classmates, teaching assistants, or your professor directly. It can also be helpful to review your notes, textbook, or class materials to gain a better understanding of the concepts being discussed.

5. How can I use my professor's comments to improve my work?

You can use your professor's comments to improve your work by addressing any areas of confusion or weakness that they have pointed out. This may involve revising your approach, seeking additional resources, or seeking help from your professor or peers. By actively incorporating their feedback, you can enhance your understanding and excel in your studies.

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