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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Variables and Constant

Constants and variables are widely used in mathematical equations and expressions. They are also commonly found in the domain of programming, where each language has its own way to differentiate between a constant and a variable. Since they have all sorts of applications, knowing their differences is a good place to start.

Question

Exercises.
Exercise 1: Write a method in Python and use it to estimate the solution of the initial value problem
dy
— 3 — 2t — 0.5у, у(0) — 1.
dt
(8)
Plot the exact solution
(9)
y(t) = 14 – 4t – 13e¬t/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
(10)
= y(a – y²)
dt
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
asymptotically stable or unstable.

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