For the linear difference equation Uz + 5uz –1 – 25up – 2 – 125u – 3 = 0 with initial conditions ug = - 1, u1 = - 40, u2 = - 75 (1) Find uz = (2) Find an explicit (non-recursive) formula for the solution of the linear difference equation with the above given initial conditions. (3) Find u13 using the formula you found in the previous part. u13 = (4) Attach your work in the following answer box either as a pdf file of your Maple sheet or as a scan of your work on paper.
For the linear difference equation Uz + 5uz –1 – 25up – 2 – 125u – 3 = 0 with initial conditions ug = - 1, u1 = - 40, u2 = - 75 (1) Find uz = (2) Find an explicit (non-recursive) formula for the solution of the linear difference equation with the above given initial conditions. (3) Find u13 using the formula you found in the previous part. u13 = (4) Attach your work in the following answer box either as a pdf file of your Maple sheet or as a scan of your work on paper.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 57E
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![The text presents a problem related to solving a linear difference equation, specifically:
For the linear difference equation
\[ u_k + 5u_{k-1} - 25u_{k-2} - 125u_{k-3} = 0 \]
with given initial conditions:
\[ u_0 = -1, \quad u_1 = -40, \quad u_2 = -75 \]
The tasks are as follows:
1. **Find \( u_3 \):**
A box is provided to enter the value of \( u_3 \).
2. **Find an explicit (non-recursive) formula for the solution of the linear difference equation with the above given initial conditions:**
A box is provided to enter the explicit formula \( u_i = \).
3. **Find \( u_{13} \) using the formula you found in the previous part:**
A box is provided to enter the value of \( u_{13} \).
4. **Attach your work in the following answer box either as a pdf file of your Maple sheet or as a scan of your work on paper.**
This assignment requires both quantitative problem-solving and the presentation of the work done.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F64c780d2-a8a0-4ff8-a74c-59396aa6e397%2Fd7f9c84c-6550-4f95-a278-392aaf487752%2F1ztk3f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The text presents a problem related to solving a linear difference equation, specifically:
For the linear difference equation
\[ u_k + 5u_{k-1} - 25u_{k-2} - 125u_{k-3} = 0 \]
with given initial conditions:
\[ u_0 = -1, \quad u_1 = -40, \quad u_2 = -75 \]
The tasks are as follows:
1. **Find \( u_3 \):**
A box is provided to enter the value of \( u_3 \).
2. **Find an explicit (non-recursive) formula for the solution of the linear difference equation with the above given initial conditions:**
A box is provided to enter the explicit formula \( u_i = \).
3. **Find \( u_{13} \) using the formula you found in the previous part:**
A box is provided to enter the value of \( u_{13} \).
4. **Attach your work in the following answer box either as a pdf file of your Maple sheet or as a scan of your work on paper.**
This assignment requires both quantitative problem-solving and the presentation of the work done.
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