Part 1: [2.5 marks] Consider the following IVP: , , The exact solution of this IVP is a) Use Euler’s method with

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Part 1: [2.5 marks]

Consider the following IVP:
,
,

The exact solution of this IVP is

a) Use Euler’s method with step size h=0.1 to approximate y(1) (you
can use Matlab and set a table of values) [0.75 mark]
b) Calculate the error bound for y(0.3) using Euler’s method and
compare the actual error. [0.75 mark]
c) Use Modified Euler’s Method (Runge-Kutta method of order two)
with step size 0.25 to approximate y(1) (you can use Matlab and set
a table of values). [1 mark]