1
$\begingroup$

$ 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.

  • 1
    The answers are now correct. As JohnD mentions, careful of your reasoning for (1). As another counterexample, $y'' y = 0$ is not linear either.2012-12-16

1 Answers 1

1

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.

  • 0
    Oh, thanks a lot! Your example pinpoints my confusion zone.2012-12-16