If r₂ and r₂ are the values of r that you found in part (a), show that every member of the family of functions y = ae1* + be 2* is also a solution. Step 1 We must decide whether 4f"(x) + 2f'(x) - 2f(x) = 0 for f(x) = aex/2 + bex. We have f'(x) = માંજ - be -X act act - be Step 2 Substituting and combining like terms, we get 4f"(x) + 2f'(x) - 2f(x) = Submit Skip (you cannot come back) ex/2 and f"(x) = -ae + || H X + be-x act +1 + bez

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Exercise (b)
If r₂ and ₂ are the values of r that you found in part (a), show that every member of the family of functions y = ae 1* + be 2* is also a solution.
Step 1
We must decide whether 4f"(x) + 2f'(x) — 2f(x) = 0 for f(x) = ae*/2 + be¯*.
We have f'(x) =
Ž
-x
- be
Step 2
Substituting and combining like terms, we get
4f"(x) + 2f'(x) - 2f(x) =
Submit Skip (you cannot come back)
-
be
and f'(x) = ae
ex/2 +1
즐
+ be-x
+ be
Transcribed Image Text:Exercise (b) If r₂ and ₂ are the values of r that you found in part (a), show that every member of the family of functions y = ae 1* + be 2* is also a solution. Step 1 We must decide whether 4f"(x) + 2f'(x) — 2f(x) = 0 for f(x) = ae*/2 + be¯*. We have f'(x) = Ž -x - be Step 2 Substituting and combining like terms, we get 4f"(x) + 2f'(x) - 2f(x) = Submit Skip (you cannot come back) - be and f'(x) = ae ex/2 +1 즐 + be-x + be
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