Linearity of differential equation

[bhanesh]

Friends I have one doubt

Below given equation is linear or non linear

:)

 

[SteamKing]

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.

 

[Chestermiller]

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).

 

[bhanesh]

But what about -5 term

 

[Chestermiller]

But what about -5 term

That's not included in the homogeneous part.

 

[Jhenrique]

Linear, because all exponents of y aren't different of +1.