Matlab Question Using the Euler's Method discussed in the lecture:a) write a function called “eulermethod" that will (1) print out the corresponding y-value for a givenx-value and (2) a plot of the original function y(x) for the following differential equation:dydxThe function will receive: the initial conditions (i.e. xo and yo), the x-value and the step-size. Recall thatthe approximate solution for yn when x = xn is given by the following equation, where h is the step-sizeand F(x,y)=y':= 1+√√y=x²y³% COMMENT SECTIONStart with the function definition shown below:endYn = Yn-1 + hF (Xn-1• Yn-1)function eulermethod (x0, y0, x, h)Test your function by computing y(3), with y(0) = 2, and the step size is 0.001.b) Now, modify the function that you created in part a) such that the function now will also plot therate of change dy/dx on the same graph, so that your graph should display both y(x) and dy/dx for0≤x≤3. Include a legend in your graph.

Introduction Euler's theorem is demonstrated under graphical theorems that provide the derivative…

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Euler's Method discu

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

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Question

Matlab Question

Using the Euler's Method discussed in the lecture:
a) write a function called “eulermethod" that will (1) print out the corresponding y-value for a given
x-value and (2) a plot of the original function y(x) for the following differential equation:
dy
dx
The function will receive: the initial conditions (i.e. xo and yo), the x-value and the step-size. Recall that
the approximate solution for yn when x = xn is given by the following equation, where h is the step-size
and F(x,y)=y':
= 1+√√y=x²y³
% COMMENT SECTION
Start with the function definition shown below:
end
Yn = Yn-1 + hF (Xn-1• Yn-1)
function eulermethod (x0, y0, x, h)
Test your function by computing y(3), with y(0) = 2, and the step size is 0.001.
b) Now, modify the function that you created in part a) such that the function now will also plot the
rate of change dy/dx on the same graph, so that your graph should display both y(x) and dy/dx for
0≤x≤3. Include a legend in your graph.

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