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Euler's Method discu

Euler's Method discu

Database System Concepts
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
Problem 1PE
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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.
Transcribed Image Text: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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