I'm having trouble understanding this for some reason...am I right about these?

xy' - 4y = 0 is linear.

y' = y - x^3 is linear.

x' + 2x - e^(-x) = 0 is non-linear.

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- Aug 27th 2013, 06:53 PMeuphonyWhat makes an ODE linear?
I'm having trouble understanding this for some reason...am I right about these?

xy' - 4y = 0 is linear.

y' = y - x^3 is linear.

x' + 2x - e^(-x) = 0 is non-linear. - Aug 27th 2013, 07:29 PMtopsquarkRe: What makes an ODE linear?
- Sep 4th 2013, 07:17 AMHallsofIvyRe: What makes an ODE linear?
Note that in the first two you are thinking of "x" as the

**independent**variable- y is a function of x. But in the last, x is the**dependent**variable- x is a function of some unnamed variable.