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Suppose that a fourth order differential equation has a solution y = -7e³x cos(x). (a) Find such a differential equation, assuming it is homogeneous and has constant coefficients. y-12y+56y"-120y +100y=0 help (equations) (b) Find the general solution to this differential equation. In your answer, use C₁, C₂, C3 and ca to denote arbitrary constants and the independent variable. Enter ci as c1, c₂ as c2, etc. y=e^(3x)(c1cosx+c2sinx)+e^(3x)(c3xcosx+c4xxsinx) help (equations)

Suppose that a fourth order differential equation has a solution y = -7e³x cos(x). (a) Find such a differential equation, assuming it is homogeneous and has constant coefficients. y-12y+56y"-120y +100y=0 help (equations) (b) Find the general solution to this differential equation. In your answer, use C₁, C₂, C3 and ca to denote arbitrary constants and the independent variable. Enter ci as c1, c₂ as c2, etc. y=e^(3x)(c1cosx+c2sinx)+e^(3x)(c3xcosx+c4xxsinx) 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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Suppose that a fourth order differential equation has a solution y = -7e³x cos(x). (a) Find such a differential equation, assuming it is homogeneous and has constant coefficients. y-12y+56y"-120y'+100y=0 help (equations) (b) Find the general solution to this differential equation. In your answer, use C₁, C₂, C3 and ca to denote arbitrary constants and the independent variable. Enter c₁ as c1, c₂ as c2, etc. y=e^(3x)(c1cosx+c2sinx)+e^(3x)(c3xcosx+c4xxsinx) help (equations)
Transcribed Image Text:Suppose that a fourth order differential equation has a solution y = -7e³x cos(x). (a) Find such a differential equation, assuming it is homogeneous and has constant coefficients. y-12y+56y"-120y'+100y=0 help (equations) (b) Find the general solution to this differential equation. In your answer, use C₁, C₂, C3 and ca to denote arbitrary constants and the independent variable. Enter c₁ as c1, c₂ as c2, etc. y=e^(3x)(c1cosx+c2sinx)+e^(3x)(c3xcosx+c4xxsinx) help (equations)
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