da 1. (a) Solve the First Order equation dy x + e for x > 0 and with initial condition y(0) = 0. (b) Solve the First Ord

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Da 1 A Solve The First Order Equation Dy X E For X 0 And With Initial Condition Y 0 0 B Solve The First Ord 1 (58.28 KiB) Viewed 27 times

da 1. (a) Solve the First Order equation dy x + e for x > 0 and with initial condition y(0) = 0. (b) Solve the First Order equation dy ly dc for all x € (-2, 2) and initial condition y(-2) = 1 and final condition y(2) = 1. What is the solution if we require y(-2) = 1 and y(2) = 0? (c) Consider the First Order equation dy = 1 + y2 dic with initial condition y(0) = 0. 0 (i) Show that F(y) := 1+ y2 satisfies a Lipschitz condition on each closed interval ( [-K/2, K/2), K > 0. (ii) Applying Picard iteration starting with yo(x) = 0 for all x € (-1,1), calculate the functions 41, 42, 43 and ya on (-1,1). (iii) Determine the first three derivatives of y at x = 0. Y