# Rudin Chapter 5 #29

#### Quantumpencil

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

Specialize exercise 28 by considering the system

$$\y'= y_{j+1} j=(1,...,k-1) y'_{k}= f(x)-\sum g_{j}(x)y_{j} where the summation runs from j=1 to j=k, and g_{j} and f are continuous real functions on [a,b], and derive a uniqueness theorem for solutions of the equation y^{k}+g_{k}(x)y^{k-1}+...+g_{2}y'+g_{1}(x)y = f(x) subject to initial conditions y(a)=c_{1}, y'(a)= c_{2}, y^{k-1}(a) = c_{k}.[\tex] 2. Relevant equations 3. The attempt at a solution 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution Related Calculus and Beyond Homework News on Phys.org #### tiny-tim Science Advisor Homework Helper Hi Quantumpencil! (you use the wrong slash: ) Specialize exercise 28 by considering the system [tex]y'= y_{j+1}, j=(1,...,k-1),\ y'_{k}= f(x)-\sum g_{j}(x)y_{j}$$ 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

$$y(a)=c_{1}, y'(a)= c_{2}, y^{k-1}(a) = c_{k}$$
Show us what you've tried, and where you're stuck, and then we'll know how to help!

#### Quantumpencil

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.

This is the link to the actual topic.

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"Rudin Chapter 5 #29"

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