How to write differential equations? Watch

kurro
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A neglected large lawn contains a certain type of weed. The area of the lawn covered by the weed at time t years is Wm^2. The rate of increase of W is directly proportional to W.

write a differential equation that is satisfied by W.

This topic always confuses me.
But is this part t = kw ?
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kurro
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mqb2766
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You have the right hand side correct, but the left hand side isn't.
The left hand side is "the rate of increase of W", how do you specify that using a derivative? The obvious answer is the right one ...
(Original post by kurro)
A neglected large lawn contains a certain type of weed. The area of the lawn covered by the weed at time t years is Wm^2. The rate of increase of W is directly proportional to W.

write a differential equation that is satisfied by W.

This topic always confuses me.
But is this part t = kw ?
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kurro
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(Original post by mqb2766)
You have the right hand side correct, but the left hand side isn't.
The left hand side is "the rate of increase of W", how do you specify that using a derivative? The obvious answer is the right one ...
dw/dt ?
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mqb2766
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That's right.
dW/dt = kW
They could have used the term "rate of change" rather than "rate of increase". If its increasing though, the derivative and hence k are positive.
(Original post by kurro)
dw/dt ?
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kurro
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(Original post by mqb2766)
That's right.
dW/dt = kW
They could have used the term "rate of change" rather than "rate of increase". If its increasing though, the derivative and hence k are positive.
Thanks so much!
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