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Suppose that the characteristic equation for a differential equation is (r – 5)²(r − 3)² = 0. Find such a differential equation, assuming it is homogeneous and has constant coefficients. Enter your answer using y, y, y", y", y" for the dependent variable and its derivatives. help (equations) Find the general solution to this differential equation. In your answer, use C₁, C2, C3 and c4 to denote arbitrary constants, use y for the dependent variable, and use x for the independent variable. Enter c₁ as "c1", c₂ as "c2", etc. Enter the solution as an equation y =?. help (equations)

Suppose that the characteristic equation for a differential equation is (r – 5)²(r − 3)² = 0. Find such a differential equation, assuming it is homogeneous and has constant coefficients. Enter your answer using y, y, y", y", y" for the dependent variable and its derivatives. help (equations) Find the general solution to this differential equation. In your answer, use C₁, C2, C3 and c4 to denote arbitrary constants, use y for the dependent variable, and use x for the independent variable. Enter c₁ as "c1", c₂ as "c2", etc. Enter the solution as an equation y =?. help (equations)

Advanced Engineering Mathematics
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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2.3.5. Ordinary Differential Equations 

Suppose that the characteristic equation for a differential equation is \((r-5)^2(r-3)^2 = 0\). Find such a differential equation, assuming it is homogeneous and has constant coefficients. Enter your answer using \(y, y', y'', y''', y''''\) for the dependent variable and its derivatives. \[ \text{[Input Box]} \quad \textit{help (equations)} \] Find the general solution to this differential equation. In your answer, use \(c_1, c_2, c_3\) and \(c_4\) to denote arbitrary constants, use \(y\) for the dependent variable, and use \(x\) for the independent variable. Enter \(c_1\) as "c1", \(c_2\) as "c2", etc. Enter the solution as an equation \(y=\)? \[ \text{[Input Box]} \quad \textit{help (equations)} \]
Transcribed Image Text:Suppose that the characteristic equation for a differential equation is \((r-5)^2(r-3)^2 = 0\). Find such a differential equation, assuming it is homogeneous and has constant coefficients. Enter your answer using \(y, y', y'', y''', y''''\) for the dependent variable and its derivatives. \[ \text{[Input Box]} \quad \textit{help (equations)} \] Find the general solution to this differential equation. In your answer, use \(c_1, c_2, c_3\) and \(c_4\) to denote arbitrary constants, use \(y\) for the dependent variable, and use \(x\) for the independent variable. Enter \(c_1\) as "c1", \(c_2\) as "c2", etc. Enter the solution as an equation \(y=\)? \[ \text{[Input Box]} \quad \textit{help (equations)} \]
Expert Solution
Step 1: We write the given characteristics equation.

(.) The characteristic equation for a differential equation is,

           open parentheses r minus 5 close parentheses squared open parentheses r minus 3 close parentheses squared space equals space 0

We find the corresponding differential equation.

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