A one-parameter family of solutions of the first-order differential equation dy/dx = xy 1/2 is y =
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A one-parameter family of solutions of the first-order differential equation dy/dx = xy1/2 is y = (1/4 x4 + c)2 for c ≥ 0. Each solution in this family is dened on (-∞, ∞). The last statement is not true if we choose c to be negative. For c = -1, explain why y = (1/4x4 – 1)2 is not a solution of the DE on the interval (-∞, ∞). Find an interval of denition I on which y = (1/4 x4 – 1)2 is a solution of the DE.
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Related Book For
A First Course in Differential Equations with Modeling Applications
ISBN: 978-1305965720
11th edition
Authors: Dennis G. Zill
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