Question: i) Calculate the approximations u 0 , u 1 , u 2 and u 3 of the Picard method for the IVP x = x

i) Calculate the approximations u₀, u₁, u₂ and u₃ of the Picard method for the IVP x = x², x (0) = 1. Then compare the approximations with the first terms of the development of Taylor around t = 0 of the solution x (t) = 1/(1 t) ii) Calculate the approximations u₀, u₁, u₂ and u₃ of the Picard method for the IVP x =(0110)x, x (0) = (1, 0) ^T .

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