Linearity of differential equation

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SUMMARY

The equation discussed is classified as a linear ordinary differential equation (ODE) with non-constant coefficients. The key factor determining its linearity is that the homogeneous part remains linear concerning the dependent variable, y. Despite the presence of a constant term (-5), it does not affect the linearity as all exponents of y are equal to +1. Comparisons to the ODE for a pendulum illustrate that while some equations can be linearized under specific conditions, this particular equation retains its linear classification.

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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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