Exercises. Exercise 1: Write a method in Python and use it to estimate the solution of the initial value problem dy = 3 – 2t – 0.5y, y(0) = 1. dt (8) Plot the exact solution (9) y(t) = 14 – 4t – 13e¬/2 together with the estimated solution obtained via the tangent line method for step sizes h = 0.1, 0.2,0.5 in the interval (0, 1]. Exercise 2: Consider the differential equation dy = y(a – y²) dt (10) for the values a = -1, a = 0 and a = 1 and determine their critical points. Sketch for each of these differen- tial equations their direction field and phase lines. Use these plots to determine whether the critical points are tiooll: hl Lunatohl

Exercises. Exercise 1: Write a method in Python and use it to estimate the solution of the initial value problem dy = 3 – 2t – 0.5y, y(0) = 1. dt (8) Plot the exact solution (9) y(t) = 14 – 4t – 13e¬/2 together with the estimated solution obtained via the tangent line method for step sizes h = 0.1, 0.2,0.5 in the interval (0, 1]. Exercise 2: Consider the differential equation dy = y(a – y²) dt (10) for the values a = -1, a = 0 and a = 1 and determine their critical points. Sketch for each of these differen- tial equations their direction field and phase lines. Use these plots to determine whether the critical points are tiooll: hl Lunatohl

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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