Rudin Chapter 5 #29

1. The problem statement, all variables and given/known data

Specialize exercise 28 by considering the system

[tex]\y'= y_{j+1} j=(1,...,k-1)
y'_{k}= f(x)-\sum g_{j}(x)y_{j} where the summation runs from j=1 to j=k, and g_{j} and f are continuous real functions on [a,b], and derive a uniqueness theorem for solutions of the equation

y^{k}+g_{k}(x)y^{k-1}+...+g_{2}y'+g_{1}(x)y = f(x)

subject to initial conditions

y(a)=c_{1}, y'(a)= c_{2}, y^{k-1}(a) = c_{k}.[\tex]



2. Relevant equations



3. The attempt at a solution
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution
 

tiny-tim

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Hi Quantumpencil! :smile:

(you use the wrong slash: :wink:)
Specialize exercise 28 by considering the system

[tex]y'= y_{j+1}, j=(1,...,k-1),\ y'_{k}= f(x)-\sum g_{j}(x)y_{j}[/tex] where the summation runs from j=1 to j=k, and g_{j} and f are continuous real functions on [a,b], and derive a uniqueness theorem for solutions of the equation

[tex]y^{k}+g_{k}(x)y^{k-1}+...+g_{2}y'+g_{1}(x)y = f(x)[/tex]

subject to initial conditions

[tex]y(a)=c_{1}, y'(a)= c_{2}, y^{k-1}(a) = c_{k}[/tex]
Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 
yeah, so I didn't realize I made this thread; it's incomplete. Could I get it locked?

The actual thread I need help on is further-down and contains the good tech + information about how I think the solution will work out.

https://www.physicsforums.com/showthread.php?t=297047

This is the link to the actual topic.
 
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