Verify that if c > 0, then the function defined piecewise by satisfies the differential equation y'

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Verify that if c > 0, then the function defined piecewise by

satisfies the differential equation y' = 4x √y for all x. Sketch a variety of such solution curves for different values of c. Then determine (in terms of a and b) how many different solutions the initial value problem y' = 4x √y, y(a) = b has.

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Differential Equations And Linear Algebra

ISBN: 9780134497181

4th Edition

Authors: C. Edwards, David Penney, David Calvis

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Question Posted: Jun 25, 2023 05:03 AM

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Verify that if c > 0, then the function defined piecewise by satisfies the differential equation y'

Question:

Jo if x² ≤ c, y(x) = {(x²-c)² if x² > c

Step by Step Answer:

The function yx satisfies the given differential equation for x 2 c since yx 4xx 2 c 4xy there ...View the full answer

Differential Equations And Linear Algebra

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