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A little stuck with trying to solve this differential equation, dx/dt = kx(x-1)
The question asks me to solve it expressing x in terms of k and t.
I've got to this far:
dx = kx (1-x) dt
1/x(1-x) dx = k dt
Put integral signs in and then integrate the left side using partial fractions to get:
ln(x) - ln(x-1)
Putting it all together:
ln(x)- ln(x-1) = 1/2 k^2 +c
What would I do know? The question asks to express x in terms of k and t?
The question asks me to solve it expressing x in terms of k and t.
I've got to this far:
dx = kx (1-x) dt
1/x(1-x) dx = k dt
Put integral signs in and then integrate the left side using partial fractions to get:
ln(x) - ln(x-1)
Putting it all together:
ln(x)- ln(x-1) = 1/2 k^2 +c
What would I do know? The question asks to express x in terms of k and t?
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#3
on the right hand side of the equation integrate with respect to t not with respect to k (it says dt not dk)
subtract logs then raise both sides to the power of e, make x the subject
subtract logs then raise both sides to the power of e, make x the subject
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#5
(Original post by Zay07)
on the right hand side of the equation integrate with respect to t not with respect to k (it says dt not dk)
subtract logs then raise both sides to the power of e, make x the subject
on the right hand side of the equation integrate with respect to t not with respect to k (it says dt not dk)
subtract logs then raise both sides to the power of e, make x the subject
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#6
(Original post by Zay07)
sorry, look at this instead
sorry, look at this instead
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(Original post by Zay07)
sorry, look at this instead
sorry, look at this instead
.So to finally solve it, I would have to plug in t=0 and x=0.2.
That would be:
0.2 = 1/1-A
A=-4.
Is that correct?
Last edited by Skar02; 25 minutes ago
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#9
(Original post by Skar02)
Thank you, that helps a lot
.
So to finally solve it, I would have to plug in t=0 and x=0.2.
That would be:
0.2 = 1/1-A
A=-4.
Is that correct?
Thank you, that helps a lot
.So to finally solve it, I would have to plug in t=0 and x=0.2.
That would be:
0.2 = 1/1-A
A=-4.
Is that correct?
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