Question: Show that the homotopy G(, x) = F(x) e F(x(0)) used in the continuation method with Euler's method and h = 1 also duplicates

Show that the homotopy
G(λ, x) = F(x) − e−λ F(x(0))
used in the continuation method with Euler's method and h = 1 also duplicates Newton's method for any x(0); that is, with x(0) = x(0), we have x(1) = x(1).

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