Suppose that the characteristic equation for a differential equation is (r−3)^2(r−5)^2=0(a) 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. (b) Find the general solution to this differential equation. In your answer, use c1,c2,c3c 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.
Suppose that the characteristic equation for a differential equation is (r−3)^2(r−5)^2=0(a) 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. (b) Find the general solution to this differential equation. In your answer, use c1,c2,c3c 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.
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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Suppose that the characteristic equation for a
(a) 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.
(b) Find the general solution to this differential equation. In your answer, use c1,c2,c3c 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.
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