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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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