Is This Fourth Order DE Nonlinear?

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Homework Help Overview

The discussion revolves around determining the order and linearity of a fourth-order differential equation presented by the original poster. The equation includes a fourth derivative and a cosine function, prompting questions about its classification as linear or nonlinear.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to classify the differential equation based on the presence of products involving derivatives and constants. Some participants seek to define what constitutes a linear differential equation, while others question the implications of multiplying derivatives by constants.

Discussion Status

The conversation has evolved from an initial assertion of nonlinearity to a reconsideration of the equation's linearity. Participants are exploring definitions and characteristics of linear differential equations, with some guidance provided on the role of constants in this context. There is an ongoing examination of specific terms and their implications for linearity.

Contextual Notes

Participants are navigating definitions and examples of linear versus nonlinear differential equations, with some uncertainty about the role of specific terms and products in the original equation. The discussion reflects a mix of interpretations and clarifications regarding the nature of the equation presented.

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Is this DE nonlinear?

Homework Statement



Determine the order and if this equation is Linear or Nonlinear.

3(d4x/dt4) + 4(dx/dt) + 9x = 3cos(3t)

The d4x is a forth order derivative. Sorry for the messiness.

Ok, this is a 4th order DE. I think it is nonlinear because of the two products (multiplying 4 time the derivative and 4 times the other derivative).

Also, the 3cos(3t) has no bearing on this because t is independent right? If the t was a y, that would cause nonlinearness.

Am I right on all this?
 
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Define linear DE
 


A linear differential equation is one in which the derivative has no function of itself (e^y, cosy, ln(y)). That is if I was differentiating with respect to y.
 


Ok.. So my equation is Linear. But you cannot have, 3a*y'. This product will make it nonlinear.
 


What's a?
 

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