Understanding Quick Differential Equation Concepts for Final Exam Preparation

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  • Thread starter Thread starter kguthrie
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SUMMARY

The discussion focuses on understanding key concepts in differential equations for final exam preparation. Participants emphasize the importance of finding derivatives to identify correct answers and suggest using the method of variation of parameters for solving equations. A specific solution, \(\frac{2e^{2t}}{1+ e^{2t}}\), is highlighted, with guidance on substituting it into the equation to derive a separable equation for \(u(t)\). This approach aids in simplifying the problem and finding the function \(y\).

PREREQUISITES
  • Basic understanding of differential equations
  • Knowledge of derivatives and their applications
  • Familiarity with the method of variation of parameters
  • Ability to manipulate and substitute functions in equations
NEXT STEPS
  • Study the method of variation of parameters in detail
  • Practice finding derivatives of complex functions
  • Explore separable differential equations and their solutions
  • Review examples of differential equations with known solutions
USEFUL FOR

Students preparing for exams in calculus or differential equations, educators teaching these concepts, and anyone seeking to enhance their problem-solving skills in mathematical analysis.

kguthrie
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Hey all, I hope this isn't against the forum rules or anything, but I'm studying for an upcoming final and had a quick question about one of the practice questions we have. I'm not sure I understand the concepts at work here, and was hoping someone could give me some insight.

http://img301.imageshack.us/img301/7656/40567729co1.png

Thanks in advance!
 
Last edited by a moderator:
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kguthrie said:
Hey all, I hope this isn't against the forum rules or anything, but I'm studying for an upcoming final and had a quick question about one of the practice questions we have. I'm not sure I understand the concepts at work here, and was hoping someone could give me some insight.

http://img301.imageshack.us/img301/7656/40567729co1.png

Thanks in advance!

Go through each answer and find the derivative. Then, check to see which satisfy the relationship in the question.
 
Last edited by a moderator:
Another method, it this weren't "multiple guess", is to use "variation of parameters".

Knowing that [tex]\frac{2e^{2t}}{1+ e^{2t}}[/tex] is a solution, set
[tex]y= u(t)\frac{2e^{2t}}{1+ e^{2t}}[/tex]
and substitute into the equation. That will give you a separable equation for u(t). Knowing that, you can find y.
 

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