Existence-Uniqueness problems.

[hermtm2]

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.

 

[Hurkyl]

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"?)

 

[hermtm2]

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.

 

[Hurkyl]

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"?

 

[Hurkyl]

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...

 

[HallsofIvy]

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.