Question 1

Consider the initial value problem
 
(Note: The exact solution is  
To apply the improved Euler method, which of the following expressions would you use for

Accepted Answer

A)  $ y-e^{2 t} y^{2} $ 
B)  $ e^{2 t} y^{2}-y $ 
C)  $ e^{2 t} y^{2} $ 
D)  $ y+e^{2 t} y^{2} $ 
A)  $ y-e^{2 t} y^{2} $ 
B)  $ e^{2 t} y^{2}-y $ 
C)  $ e^{2 t} y^{2} $ 
D)  $ y+e^{2 t} y^{2} $

Question 2

Consider the initial value problem   This question relates to using the backward Euler method to approximate the solution at t = 0.2, namely = y(0.2), using a step size of h = 0.02.
Which of these identifications are correct when setting up the backward Euler method? Select all that apply.

Accepted Answer

A)  $ t_{0}=0 $ 
B)  $ y_{0}=0 $ 
C)  $ y_{0}=1 $ 
D)  $ t_{1}=1 $ 
E)  $ t_{1}=0.2 $ 
A)  $ t_{0}=0 $ 
B)  $ y_{0}=0 $ 
C)  $ y_{0}=1 $ 
D)  $ t_{1}=1 $ 
E)  $ t_{1}=0.2 $

Question 3

Given the initial value problem   = 9y + 6t, y(0) = 5, how many steps n are needed for the Euler method to find an approximation for y(1.77) using a step size of h = 0.03?
n ________

Accepted Answer

The answer of Given the initial value problem  ...

Consider the initial value problem (Note: The exact solution is To apply the improved Euler method, which of the following expressions would you use for

Consider the initial value problem This question relates to using the backward Euler method to approximate the solution at t = 0.2, namely = y(0.2), using a step size of h = 0.02. Which of these identifications are correct when setting up the backward Euler method? Select all that apply.

Given the initial value problem = 9y + 6t, y(0) = 5, how many steps n are needed for the Euler method to find an approximation for y(1.77) using a step size of h = 0.03? n ________

Introduction

First-Order Differential Equations

Second-Order Linear Differential Equations

Higher-Order Linear Differential Equations

Series Solutions of Second-Order Linear Equations

The Laplace Transform

Systems of First-Order Linear Equations

Nonlinear Differential Equations and Stability

Partial Differential Equations and Fourier Series

Boundary Value Problems and Sturm-Liouville Theory

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Exam 8: Numerical Methods