Solve Bonus Problem with Power Series: (x^2)(y")+y=0 | Help Needed!"

  • Thread starter momen salah
  • Start date
In summary, bonus problems are additional tasks or challenges given to students or researchers to further test and expand their knowledge and skills. They exist to provide an opportunity for individuals to push themselves beyond their comfort zone and demonstrate their understanding and abilities. Bonus problems differ from regular assignments in terms of difficulty, approach, and point value. They may be completed individually or in groups, depending on the instructions given. Bonus problems can be found in any subject or field, although they often involve experimental design, data analysis, or theoretical problem-solving in the context of science.
  • #1
momen salah
7
0
hi guys it's me you helped me last time in my bonus problem(thank's for that) i need help again naw please it's a two marks bonus problem:

solve using power series:
(x^2)(y")+y=0

after solving it i stopped at :

an[n^2-n+1]=0
 
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  • #2
Try a solution of the form
[tex]y= \sum_{n=0}^{\infty} a_nx^{n+i}[/tex]

where i is not necessarily positive nor even an integer. Look at the lowest powers after you have put that into the differential equation (and assume a0 is NOT 0) in order to determine i.
 

1. What is a bonus problem?

A bonus problem is an extra task or challenge that is given to students or researchers in addition to their regular coursework or research projects. It is usually more difficult or complex than the standard assignments and is meant to further test and expand the participants' knowledge and skills.

2. Why do bonus problems exist?

Bonus problems exist to provide an additional opportunity for students or researchers to push themselves beyond their comfort zone and demonstrate their understanding and abilities in a particular subject or field. They also serve as a way for instructors or supervisors to gauge the level of aptitude and potential of their students or employees.

3. How are bonus problems different from regular assignments?

Bonus problems differ from regular assignments in that they are not mandatory and are usually more challenging and open-ended. They may also require a different approach or use of additional resources compared to standard assignments. Additionally, bonus problems often have a higher point value and can potentially boost a student's grade or a researcher's evaluation.

4. Can bonus problems be done in groups or are they meant to be completed individually?

This may vary depending on the specific instructions given by the instructor or supervisor. Some bonus problems may be intended for individual completion only, while others may allow for collaboration with classmates or colleagues. It is important to clarify this with the person giving the bonus problem.

5. Are bonus problems only found in scientific fields?

No, bonus problems can exist in any subject or field, including the humanities and arts. They may take the form of additional writing prompts, creative projects, or research inquiries. However, in the context of science, bonus problems often involve experimental design, data analysis, or theoretical problem-solving.

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