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**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**