I am reading through my Diff Eqs Text and I follow most of the lingo. However I am just a tad confused by the statement:(adsbygoogle = window.adsbygoogle || []).push({});

An nth order ODE is said to be linear if F is linear in y,y',...y^(n)

Then it gives the example:

[tex]a_n(x)\frac{d^ny}{dx^n}+a_{n-1}(x)..+a_0(x)y=g(x)[/tex]

It then says: 'On the left-hand side of the above equation the dependent variable y and all of its derivatives, y,y',y'',...y[itex]^n[/itex] are of the first degree.

Clearly I missed something in Calc. If n=2, I have: [tex]\frac{d^2y}{dx^2}[/tex]

Why is this linear if n=2?

Thanks,

Casey

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# Homework Help: Question about linearity

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