# First Order Differential Equations by Separating Variables

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#1
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1 month ago
#2
(Original post by Silentieyes)
What's your question, and what have you tried so far?
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1 month ago
#3
Yes I could help
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#4
so far i only did this much
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#5
(Original post by 15Characters...)
What's your question, and what have you tried so far?
to prove that R = e^1/250 θ
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1 month ago
#6
(Original post by Silentieyes)
to prove that R = e^1/250 θ
There is only one constant. They (it) do not cancel
It's found using the initial conditions.

Also remember ln is the inverse of an exponential so the left hand side is ...
Last edited by mqb2766; 1 month ago
1
1 month ago
#7
(Original post by Silentieyes)
so far i only did this much
I'm not sure if the other poster resolved your difficulties, but I'll add something just incase.

You are not correct that the constants cancel out, because the constants on the left and right hand side need not be equal. Instead you could have written something like

where are arbitrary constants, not necessarily equal. However we do not really have two free constants to set, as we can move to the right hand side to get

where is our single arbitrary constant, which is then set by applying the initial conditions.

In practice you should just put a constant on one side in the first place, like in Eq. (*).
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#8
Solved it! thank you so much everyone
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#9
(Original post by 15Characters...)
I'm not sure if the other poster resolved your difficulties, but I'll add something just incase.

You are not correct that the constants cancel out, because the constants on the left and right hand side need not be equal. Instead you could have written something like

where are arbitrary constants, not necessarily equal. However we do not really have two free constants to set, as we can move to the right hand side to get

where is our single arbitrary constant, which is then set by applying the initial conditions.

In practice you should just put a constant on one side in the first place, like in Eq. (*).

but i will take your advice for upcoming practices. thank you so much for helping me
0
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