I have a Differential Equation question... I've just started, so the question is quite simple:

How do I know if a function is linear or not?

For instance: (x-1)y'' + yxy' - cos x = 1. Is this a linear or non linear function?

Question

I have a Differential Equation question... I've just started, so the question is quite simple:

How do I know if a function is linear or not?

For instance: (x-1)y'' + yxy' - cos x = 1. Is this a linear or non linear function?

anonymous · Answer

What function?

anonymous · Answer

In general, a function is linear if it satisfies:
f(a+b) = f(a)+f(b)
and 
f(kx) = kf(x)
where k is a real number.

goformit100 · Answer

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amistre64 · Answer

(x-1)y'' + yxy' - cos x = 1

as long as none of the y parts have an exponent greater then 1, or are modified by trig or ln or something unnatural ... it should be good

amistre64 · Answer

y'' is a derivative, of order 2
y' is a derivative of order 1

y is a function that the derivatives came from.

amistre64 · Answer

and in this case, it looks like the y' y part is pushing this to nonlinear