Problem 16 Consider the following modification of the initial value problem in Example 2: y" - y' +0.25y = 0, y(0) = 2, y'(0) = b. - Find the solution as a function of b, and then determine the critical value of b that separates solutions that grow positively from those that eventually grow negatively.

Advanced Engineering Mathematics
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ISBN:9780470458365
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Chapter2: Second-order Linear Odes
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Problem 16
Consider the following modification of the initial value problem in Example 2:
y" - y' +0.25y = 0,
y(0) = 2, y'(0) = b.
Find the solution as a function of b, and then determine the critical value of b that separates
solutions that grow positively from those that eventually grow negatively.
Transcribed Image Text:Problem 16 Consider the following modification of the initial value problem in Example 2: y" - y' +0.25y = 0, y(0) = 2, y'(0) = b. Find the solution as a function of b, and then determine the critical value of b that separates solutions that grow positively from those that eventually grow negatively.
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