What is the solution to the equation y''' + 4y'' + 4y'=0?

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The discussion revolves around solving the third-order ordinary differential equation (ODE) given by y''' + 4y'' + 4y' = 0. Participants are exploring methods for finding a solution and questioning the validity of their approaches.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster inquires about the appropriate method to solve the equation and suggests a transformation to a characteristic equation. Another participant considers treating the problem as if it were a second-order ODE, expressing uncertainty about the general applicability of this approach.

Discussion Status

Some participants confirm the original poster's transformation into a characteristic equation, indicating a shared understanding of that aspect. However, there is no explicit consensus on the overall method or approach to solving the ODE.

Contextual Notes

There is uncertainty regarding the effectiveness of treating the third-order ODE as a second-order ODE, which raises questions about the assumptions underlying this approach.

RadiationX
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what method do i employ to solve this?

[tex]y''' + 4y'' + 4y'=0[/tex]

does the above lead to something like this?

[tex]r^3 +4r^2 +4r=0[/tex]
 
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Approaching this problem like if it was a 2nd order ODE yield a solution that satisfied the ODE. But I am not sure if this will work all the time.
 
dextercioby said:
Yes,it does.

Daniel.


thx i thought that it did
 

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