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Let's consider the following nonhomogeneous first-order ODE: dy = dt 3.2y - 12t We first investigated how to solve such an ODE with the use of the Linearity Principle, which will be the focus of this question. a.) Find the solution, yh, to the homogeneous reduction. Be sure to show all work. b.) Craft an appropriate guess for y, and find the appropriate coefficient. Be sure to show all work. c.) Write the general solution to this ODE. d.) Suppose we replaced the -12t in the above ODE with 62t2. What would be an appropriate guess for yp? Do NOT solve for it... just tell me what the guess should be and why it is appropriate.

Let's consider the following nonhomogeneous first-order ODE: dy = dt 3.2y - 12t We first investigated how to solve such an ODE with the use of the Linearity Principle, which will be the focus of this question. a.) Find the solution, yh, to the homogeneous reduction. Be sure to show all work. b.) Craft an appropriate guess for y, and find the appropriate coefficient. Be sure to show all work. c.) Write the general solution to this ODE. d.) Suppose we replaced the -12t in the above ODE with 62t2. What would be an appropriate guess for yp? Do NOT solve for it... just tell me what the guess should be and why it is appropriate.

Advanced Engineering Mathematics
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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Let's consider the following nonhomogeneous first-order ODE: = = 3.2y - 12t dy dt We first investigated how to solve such an ODE with the use of the Linearity Principle, which will be the focus of this question. a.) Find the solution, yh, to the homogeneous reduction. Be sure to show all work. b.) Craft an appropriate guess for y, and find the appropriate coefficient. Be sure to show all work. c.) Write the general solution to this ODE. d.) Suppose we replaced the -12t in the above ODE with 62t2. What would be an appropriate guess for yp? Do NOT solve for it... just tell me what the guess should be and why it is appropriate.
Transcribed Image Text:Let's consider the following nonhomogeneous first-order ODE: = = 3.2y - 12t dy dt We first investigated how to solve such an ODE with the use of the Linearity Principle, which will be the focus of this question. a.) Find the solution, yh, to the homogeneous reduction. Be sure to show all work. b.) Craft an appropriate guess for y, and find the appropriate coefficient. Be sure to show all work. c.) Write the general solution to this ODE. d.) Suppose we replaced the -12t in the above ODE with 62t2. What would be an appropriate guess for yp? Do NOT solve for it... just tell me what the guess should be and why it is appropriate.
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