y = 2ry, y(1) = 1; y(1.5). Find an explicit solution of the initial value problem. (i) Use Euler's method to obtain a 4-decimal approximation of the problem with h =0.1. (ii) Analyse the comparison between the analytical solution and the nu- merical solution.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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For a
(a)
Given an initial value problem
y =2ry,
y(1) = 1;
y(1.5).
(1)
Find an explicit solution of the initial value problem.
(i)
Use Euler's method to obtain a 4-decimal approximation of the problem
with h =0.1.
(ii)
Analyse the comparison between the analytical solution and the nu-
merical solution.
(b)
The Maclaurin series of sinx is given by
sin r
1!
Use the above expansion to check if x = 0 is an ordinary or a singular point of
the differential equation
xy + (sinx)y= 0.
Transcribed Image Text:(a) Given an initial value problem y =2ry, y(1) = 1; y(1.5). (1) Find an explicit solution of the initial value problem. (i) Use Euler's method to obtain a 4-decimal approximation of the problem with h =0.1. (ii) Analyse the comparison between the analytical solution and the nu- merical solution. (b) The Maclaurin series of sinx is given by sin r 1! Use the above expansion to check if x = 0 is an ordinary or a singular point of the differential equation xy + (sinx)y= 0.
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