Suppose that the characteristic equation for a differential equation is (r – 8)²(r + 7) = 0. A. Find such a differential equation, assuming it is homogeneous and has constant coefficients. Write your answer using y, y', y" and y" for the dependent variable and its derivatives. B. Use the characteristic equation to find the general solution to this differential equation. In your answer, use c1, c2 and c3 to denote arbitrary constants, use y for the dependent variable, and use x for the independent variable.
Suppose that the characteristic equation for a differential equation is (r – 8)²(r + 7) = 0. A. Find such a differential equation, assuming it is homogeneous and has constant coefficients. Write your answer using y, y', y" and y" for the dependent variable and its derivatives. B. Use the characteristic equation to find the general solution to this differential equation. In your answer, use c1, c2 and c3 to denote arbitrary constants, use y for the dependent variable, and use x for the independent variable.
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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Transcribed Image Text:Suppose that the characteristic equation for a differential equation is (r – 8)²(r + 7) = 0.
A. Find such a differential equation, assuming it is homogeneous and has constant coefficients. Write your answer using y, y', y" and y" for the dependent
variable and its derivatives.
B. Use the characteristic equation to find the general solution to this differential equation. In your answer, use c1, c2 and c3 to denote arbitrary constants, use y for
the dependent variable, and use x for the independent variable.
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