Is (1+y^2) d^2y/dt^2 + t dy/dt + y = et a Linear Equation?

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Discussion Overview

The discussion centers around the classification of the differential equation (1+y^2) d^2y/dt^2 + t dy/dt + y = e^t, specifically whether it is a linear equation or not. The scope includes theoretical considerations of linearity in differential equations.

Discussion Character

  • Debate/contested

Main Points Raised

  • Some participants argue that the presence of y squared indicates that the equation is not linear.
  • Others reinforce this view by stating that the equation contains a non-linear function of the dependent variable, y.

Areas of Agreement / Disagreement

Participants generally agree that the equation is not linear, citing the presence of y squared as the primary reason. However, the discussion remains focused on this specific aspect without further exploration of alternative interpretations.

patrickbotros
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(1+y2) d2y/(dt2) + t dy/dt +y = et
 
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I think its not linear, there's y squared
 
No, it's not.
 
It is not because, as Leonita said, it has a non-linear function of the dependent variable, y.
 

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