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where Φ[yi(x)] =



ordinary linear differential equations Consider a of n continuous functions yi(x) [i = 1,2,3,...,n], each of which is differentiable at least n times. Then if there exist a set of constants λi that are not all zero such that λiy1(x)+λ2y2(x)+···+λnyn(x) = 0, (1) then we say that the set of functions {yi(x)} are linearly dependent. If the only solution to eq. (1) is λi = 0 for all i, then the set of functions {yi(x)} are linearly independent. The Wronskian matrix is defined as

Year: 2014
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