Linearity of differential equation

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Discussion Overview

The discussion revolves around the classification of a given differential equation as linear or non-linear. Participants explore the criteria for linearity, referencing specific terms and coefficients in the equation.

Discussion Character

  • Debate/contested

Main Points Raised

  • Some participants argue that the equation is non-linear due to the presence of a cos x coefficient, drawing a comparison to the non-linear ordinary differential equation for a pendulum.
  • Others assert that the equation is linear, stating that it is considered a linear ordinary differential equation with non-constant coefficients, emphasizing the importance of the homogeneous part being linear with respect to the dependent variable.
  • A participant questions the role of a -5 term in the equation, prompting further clarification on its inclusion in the classification.
  • Another participant states that the equation is linear because all exponents of the dependent variable y are equal to +1.

Areas of Agreement / Disagreement

Participants express differing views on the linearity of the equation, with no consensus reached regarding its classification.

Contextual Notes

Participants reference specific terms and coefficients in the equation, but the discussion does not resolve the implications of these terms on the overall classification.

bhanesh
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Friends I have one doubt

Below given equation is linear or non linear

1387027772743.jpg


:)
 
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It's non-linear, because of the cos x coefficient. Compare it to the ODE for a pendulum, which is non-linear, but can be linearized if small deflections are assumed.
 
bhanesh said:
Friends I have one doubt

Below given equation is linear or non linear

View attachment 64770

:)
Mathematically,the equation you wrote is considered a linear ordinary differential equation with non-constant coefficients. It is considered linear if the homogeneous part is linear with respect to the dependent variable (in this case y).
 
But what about -5 term
 
bhanesh said:
But what about -5 term
That's not included in the homogeneous part.
 
Linear, because all exponents of y aren't different of +1.
 

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