It says on Wikipedia in the article on differential equations that:(adsbygoogle = window.adsbygoogle || []).push({}); 'a differential equation is linear if the unknown function and its derivatives appear to the power 1 (products are not allowed) and nonlinear otherwise'

Are these products between any of the variables that appear? So, are products between derivatives, the unknown function AND the independent variable not allowed or is it just between the derivatives and unknown functions?

In a book on ODEs I found in the library, it says:

..the general form linear ordinary differential equation of order n is

[tex]a_0(x)y^{(n)}+a_1(x)y^{(n-1)}+...}a_n(x)y=g(x)[/tex]

[tex]a_n(x)[/tex] are coefficients which are functions of x...so can these be any random function of x that doesn't really relate to the unknown function we're trying to find? Are they usually constants?

And what is the g(x) on the RHS?

Thanks

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# Question about linear ODEs

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