Just a simple question:

Is cosxdy/dx = x non-linear because of cosx?

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- September 14th 2010, 04:30 AMCookieCLinear/non-linear
Just a simple question:

Is cosxdy/dx = x non-linear because of cosx? - September 14th 2010, 05:01 AMCaptainBlack
- September 14th 2010, 05:10 AMJester
Any first ODE that can be written as

i.e. linear in both and is a linear ODE. Your ODE is

so it's - September 14th 2010, 06:23 AMCaptainBlack
- September 14th 2010, 06:36 AMJester
But aren't you assuming two independent solutions (for a first order ODE?).

- September 14th 2010, 06:56 AMCaptainBlack
- September 14th 2010, 07:54 AMAckbeet
According to the wiki, a linear differential equation is of the form

where is a linear differential operator.

That is, you apply CB's definition of linearity to the*operator*, not necessarily to the entire equation. If the equation is homogeneous, they'll turn out to be the same thing. But even a non-homogeneous linear DE does not obey the superposition principle except in its homogeneous solution.

This is my understanding. - September 14th 2010, 07:57 AMCaptainBlack