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Consider the following differential equation. 4y" + 2y' - 2y = 0 Exercise (a) For what values of r does the functlon y - ex satisfy the equation? Click here to begin! Exercise (b) If r, and r are the values of r that you found in part (a), show that every member of the family of functions y = ae'ix + be'2x is also a solution. Step 1 We must decide whether 4f"(x) + 2f'(x) - 2f(x) - 0 for f(x) = ae/2 + be-x. We have f'(x) = and f"(x) =

Consider the following differential equation. 4y" + 2y' - 2y = 0 Exercise (a) For what values of r does the functlon y - ex satisfy the equation? Click here to begin! Exercise (b) If r, and r are the values of r that you found in part (a), show that every member of the family of functions y = ae'ix + be'2x is also a solution. Step 1 We must decide whether 4f"(x) + 2f'(x) - 2f(x) - 0 for f(x) = ae/2 + be-x. We have f'(x) = and f"(x) =

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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This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Consider the following differential equation. 4y" + 2y'- 2y 0 Exercise (a) For what values of r does the function y = ex satisfy the equation? Click here to begin! Exercise (b) If ri and r, are the values of r that you found in part (a), show that every member of the family of functions y = ae'1x + be'2x is also a solution. Step 1 We must decide whether 4f "(x) + 2f'(x) - 2f(x) = 0 for f(x) = aex/2 + be-X. We have f'(x) = and f"(x) = Submit Skip (you cannot come back)
Transcribed Image Text:This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Consider the following differential equation. 4y" + 2y'- 2y 0 Exercise (a) For what values of r does the function y = ex satisfy the equation? Click here to begin! Exercise (b) If ri and r, are the values of r that you found in part (a), show that every member of the family of functions y = ae'1x + be'2x is also a solution. Step 1 We must decide whether 4f "(x) + 2f'(x) - 2f(x) = 0 for f(x) = aex/2 + be-X. We have f'(x) = and f"(x) = Submit Skip (you cannot come back)
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