Using the analogous logic for getting particular solutions of non homogeneous difference equations, find particular solutions to the following equations. Explain your reasoning. Remember, you are not guessing, you are rigorously developing the solution. y(k+3)+y(k+2)+y(k+1)+3y(k)=5 y(k+2)+3y(k+1)+2y(k)= k y(k+2)+y(k+1)+y(k)=(0.5)* y(k+2)+3y(k+1)+2y(k)=(-1)* y(k+1)+ y(k)=2 sin(k)=(e¹ - e¯*)/i On the last equation, you can find a particular solution by finding particular solutions for each exponential (as in the third equation in the set) and adding together, or you can use sum of constant times sine and constant times cosine added together, then you need to use trig identities.
Using the analogous logic for getting particular solutions of non homogeneous difference equations, find particular solutions to the following equations. Explain your reasoning. Remember, you are not guessing, you are rigorously developing the solution. y(k+3)+y(k+2)+y(k+1)+3y(k)=5 y(k+2)+3y(k+1)+2y(k)= k y(k+2)+y(k+1)+y(k)=(0.5)* y(k+2)+3y(k+1)+2y(k)=(-1)* y(k+1)+ y(k)=2 sin(k)=(e¹ - e¯*)/i On the last equation, you can find a particular solution by finding particular solutions for each exponential (as in the third equation in the set) and adding together, or you can use sum of constant times sine and constant times cosine added together, then you need to use trig identities.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 4CEXP
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Transcribed Image Text:Problem 3
Using the analogous logic for getting particular solutions of non homogeneous
difference equations, find particular solutions to the following equations. Explain
your reasoning. Remember, you are not guessing, you are rigorously developing the
solution.
y(k+3)+y(k+2)+y(k+1)+3y(k)=5
y(k+2)+3y(k+1)+2y(k)= k
y(k+2)+y(k+1)+y(k)=(0.5)*
y(k+2)+3y(k+1)+2y(k)=(-1)*
y(k+1)+ y(k)=2 sin(k)=(e-e)/i
On the last equation, you can find a particular solution by finding particular
solutions for each exponential (as in the third equation in the set) and adding
together, or you can use sum of constant times sine and constant times cosine added
together, then you need to use trig identities.
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