see pictures below. Consider the equation: ay" + by' + cy = g (t) where a, b, and c are positive constants.1. If Y1 (t) and Y2 (t) are solutions, show that Y1 (t) – Y2 (t)2. If g (t) = d, where d is a Real number, show that every solution approaches3. If g (t) = d, where d is a Real number like in part 2, what happens if c =→ 0 as t → O.as t → ∞ .0? Why?Hint: You may take for granted that under the original conditions (a, b, and c are positive constants), all homogeneoussolutions approach 0 as t → ∞.

Name: see pictures below. Consider the equation: ay" + by' + cy = g (t) wher
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Description: see pictures below. Consider the equation: ay" + by' + cy = g (t) where a, b, and c are positive constants.1. If Y1 (t) and Y2 (t) are solutions, show that Y1 (t) – Y2 (t)2. If g (t) = d, where d is a Real number, show that every solution approaches3

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Consider the equation: ay" + by' + cy = g (t) where a, b, and c are positive constants. 1. If Y1 (t) and Y2 (t) are solutions, show that Y1 (t) – Y2 (t) → 0 as t → ∞. 2. If g (1) = d, where d is a Real number, show that every solution approaches as t → 0

Consider the equation: ay" + by' + cy = g (t) where a, b, and c are positive constants. 1. If Y1 (t) and Y2 (t) are solutions, show that Y1 (t) – Y2 (t) → 0 as t → ∞. 2. If g (1) = d, where d is a Real number, show that every solution approaches as t → 0

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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see pictures below.

Consider the equation: ay" + by' + cy = g (t) where a, b, and c are positive constants.
1. If Y1 (t) and Y2 (t) are solutions, show that Y1 (t) – Y2 (t)
2. If g (t) = d, where d is a Real number, show that every solution approaches
3. If g (t) = d, where d is a Real number like in part 2, what happens if c =
→ 0 as t → O.
as t → ∞ .
0? Why?
Hint: You may take for granted that under the original conditions (a, b, and c are positive constants), all homogeneous
solutions approach 0 as t → ∞.

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