W [ ϕ 1, ϕ 2] ( t) = | ϕ 1 ( t) ϕ 2 ( t) ϕ 1 ′ ( t) ϕ 2 ′ ( t) |. of the solutions might be mentioned. Case II: Likewise, when discussing two solutions. ϕ 1 ( t) = [ x 1 ( t) y 1 ( t)] ϕ 2 ( t) =
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Given a set of n functions f1 , , fn, the Wronskian W (f1, , fn) is given by: The Wronskian can be used to determine whether a set of differentiable functions is linearly independent on a given
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If y1(t) y 1 ( t) and y2(t) y 2 ( t) are two solutions to. y′′+p(t)y′ +q(t)y = 0 y ″ + p ( t) y ′ + q ( t) y = 0. then the Wronskian of the two solutions is. W (y1,y2)(t) = W (y1,y2)(t0)e−∫ t
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