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Question 3 (a) Given an initial value problem y = 2xy, y(1) = 1; у (1.5). (i) Find an explicit solution of the initial value problem. Use Euler's method to obtain a 4-decimal approximation of the problem with h = 0.1. (i) (ii) Analyse the comparison between the analytical solution and the nu- merical solution. (b) The Maclaurin series of sinx is given by sinx 1! + 3! 5! +. 7! Use the above expansion to check if x = 0 is an ordinary or a singular point of the differential equation xy +(sinx) y = 0.

Question 3 (a) Given an initial value problem y = 2xy, y(1) = 1; у (1.5). (i) Find an explicit solution of the initial value problem. Use Euler's method to obtain a 4-decimal approximation of the problem with h = 0.1. (i) (ii) Analyse the comparison between the analytical solution and the nu- merical solution. (b) The Maclaurin series of sinx is given by sinx 1! + 3! 5! +. 7! Use the above expansion to check if x = 0 is an ordinary or a singular point of the differential equation xy +(sinx) y = 0.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.1: Equations
Problem 62E
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Question 3 (а) Given an initial value problem y = 2xy, y(1) = 1; y (1.5). (1) Find an explicit solution of the initial value problem. (ii) Use Euler's method to obtain a 4-decimal approximation of the problem with h = 0.1. Analyse the comparison between the analytical solution and the nu- merical solution. (b) The Maclaurin series of sinx is given by sinx = 1! 3! 5! 7! Use the above expansion to check if x = 0 is an ordinary or a singular point of the differential equation xy + (sin.x) y = 0.
Transcribed Image Text:Question 3 (а) Given an initial value problem y = 2xy, y(1) = 1; y (1.5). (1) Find an explicit solution of the initial value problem. (ii) Use Euler's method to obtain a 4-decimal approximation of the problem with h = 0.1. Analyse the comparison between the analytical solution and the nu- merical solution. (b) The Maclaurin series of sinx is given by sinx = 1! 3! 5! 7! Use the above expansion to check if x = 0 is an ordinary or a singular point of the differential equation xy + (sin.x) y = 0.
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