Existence-Uniqueness problems.

  • Thread starter hermtm2
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In summary, the conversation discusses a problem involving an integral that the speaker is struggling to solve. They ask for help and mention the Existence-Uniqueness Theorem, which guarantees a unique solution for certain differential equations. The speaker is unsure how to apply it in this situation and asks for clarification on the theorem's hypotheses.
  • #1
hermtm2
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Hello.

I can't do Integral(1/ln(y)dy). Can you guys help me out?

This is the original problem.

In each of these IVPs, determine whether or not the Existence-Uniqueness Theorom guarantees a unique solution.

1. dy/dx = ln(y), y(0)=0
2. dy/dx = ln(y), y(1)=1

Thanks.
 
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  • #2
hermtm2 said:
Hello.

I can't do Integral(1/ln(y)dy).
Why does that matter? What is the "Existence-Uniqueness theorem"?

(I assume by "do" you mean "rewrite as an algebraic combination of elementary functions"?)
 
  • #3
Solve for differential equation to find a unique solution. In order to solve the equation, I have to integrate it but I don't know how to do it.
 
  • #4
hermtm2 said:
In order to solve the equation, I have to integrate it but I don't know how to do it.
Then find another way to answer the question you were asked!

What is the "Existence-Uniqueness theorem"?
 
  • #5
P.S. even if you could rewrite this integral in terms of elementary functions, I don't think that would answer the question you were asked...
 
  • #6
Hurkyl's point is that you do NOT need to solve the equation to "determine whether or not the Existence-Uniqueness Theorom guarantees a unique solution."

Answer his first question: What is the "Existence-Uniqueness Theorem"? What are it hypotheses.
 

1. What are existence-uniqueness problems?

Existence-uniqueness problems are mathematical problems in which one seeks to find a solution that satisfies a given set of conditions. These problems are typically solved using differential equations and are important in many areas of science and engineering.

2. Why are existence-uniqueness problems important?

Existence-uniqueness problems are important because they help us understand the behavior of systems and phenomena in the natural world. By finding solutions to these problems, we can make predictions and better understand the underlying principles governing complex systems.

3. How are existence-uniqueness problems solved?

Existence-uniqueness problems are typically solved using mathematical techniques such as integration, differentiation, and numerical methods. These methods help us find solutions that satisfy the given conditions and provide insights into the behavior of the system.

4. What are some real-world applications of existence-uniqueness problems?

Existence-uniqueness problems have many real-world applications, such as predicting the behavior of weather patterns, understanding the dynamics of chemical reactions, and modeling financial markets. These problems are also important in fields such as physics, biology, and engineering.

5. Are there any challenges associated with solving existence-uniqueness problems?

Yes, there are several challenges associated with solving existence-uniqueness problems. One of the main challenges is the complexity of the problems, which often require advanced mathematical techniques and computational resources. Another challenge is that real-world systems are often nonlinear, making it difficult to find exact solutions to these problems.

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