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$$ y''+3ty'+2y=3\sin(t) $$

So below is my description of the equation above, let me know whether they are correct or not:

(1) it's linear (no square or higher power)

(2) it's second order (obvious)

(3) it's non autonomous (as it depends on t)

(4) it's non-constant coefficient (because it has 3t)

(5) it's non homogenous (because one 3sin(t) on the right hand side)

NOT a homework, just me making up a question and trying to understand catagrization.

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Oh, yes, thanks. Am i right with them now? I edited seconds ago with some justifications. Thanks a lot! – user48601 Dec 16 '12 at 18:50
The answers are now correct. As JohnD mentions, careful of your reasoning for (1). As another counterexample, $y'' y = 0$ is not linear either. – process91 Dec 16 '12 at 18:53
up vote 1 down vote accepted

Sounds like you are just unfamiliar with the terminology in ODEs. This should help.

Beware on your reasoning for (1). The equation $y''+y\sin y=0$ is nonlinear, yet $y''+t^{99}y=0$ is linear.

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Oh, thanks a lot! Your example pinpoints my confusion zone. – user48601 Dec 16 '12 at 18:57

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