A differential equation may possess more than one family of solutions (a) Plot different members of the families y 1 (x) x 2 c 1 and y 2 (x) x 2 c 2 (b) Verify that y 1 (x) and y 2 (x) are two solutions of the nonlinear first order differential equation (y ') 2 4x 2 (c) Construct a piece wise defin...

a b When y x 2 c 1 y 2x and y 2 4 ...

A differential equation may possess more than one family of solutions. (a) Plot different members of the

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A differential equation may possess more than one family of solutions.

(a) Plot different members of the families y = ϕ₁(x) = x² + c₁ and y = ϕ₂(x) = -x² + c₂.

(b) Verify that y = ϕ₁(x) and y = φ₂(x) are two solutions of the nonlinear first-order differential equation (y')² = 4x².

(c) Construct a piece wise-defined function that is a solution of the nonlinear DE in part (b) but is not a member of either family of solutions in part (a).

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A First Course in Differential Equations with Modeling Applications

ISBN: 978-1305965720

11th edition

Authors: Dennis G. Zill

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Question Posted: Jul 10, 2018 12:43 PM

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A differential equation may possess more than one family of solutions. (a) Plot different members of the

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A First Course in Differential Equations with Modeling Applications

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