MEI C4 Qs 7i) Watch

Newyork Nagaram...
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#1
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I Just don't understand the mark scheme!

http://www.mei.org.uk/files/papers/c410ja_4754.pdf

Thx
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ttoby
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You need to take the equation given, x=\dfrac{1}{1+e^{-t}} and calculate dx/dt and x(1-x) to check if they give the same answer, as well as checking the initial conditions.


The easiest way of doing it is to calculate (1-x) in terms of t by adding fractions, then work out x(1-x). Then calculate dx/dt using the chain rule.
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Newyork Nagaram...
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(Original post by ttoby)
You need to take the equation given, and calculate dx/dt and x(1-x) to check if they give the same answer, as well as checking the initial conditions.


The easiest way of doing it is to calculate (1-x) in terms of t by adding fractions, then work out x(1-x). Then calculate dx/dt using the chain rule.
How? ... What fractions?
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Farhan.Hanif93
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(Original post by Newyork Nagaram...)
How? ... What fractions?
1-x \equiv 1 - \dfrac{1}{1+e^{-t}} \equiv \dfrac{1+e^{-t}}{1+e^{-t}} - \dfrac{1}{1+e^{-t}}.
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RK92
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what you do now is put that solution x=1/(1+e^-t) into the right hand side of dx/dt=x(1-x)

if you then show that the right hand side you obtained by putting x into the equation is the same as just differentiating the x solution you were given, then the left hand side and right hand side are equal so the solution x=1/(1+e^-t) satisfies the differential equation.

lol neg
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Newyork Nagaram...
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(Original post by Farhan.Hanif93)
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This is the Bit i don't Get... How is 1-x= 1-(1/1+e^-t)??
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Farhan.Hanif93
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(Original post by Newyork Nagaram...)
This is the Bit i don't Get... How is 1-x= 1-(1/1+e^-t)??
You're told to verify that the differential equation \dfrac{dx}{dt}=x(1-x) is satisfied by x=\dfrac{1}{1-e^{-t}} so you're gonna have to sub that in, in place of x, in the RHS and also calculate the derivative directly for the LHS and show that they are equal.
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ttoby
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(Original post by Newyork Nagaram...)
This is the Bit i don't Get... How is 1-x= 1-(1/1+e^-t)??
You're told that x=\dfrac{1}{1+e^{-t}} so 1-x=1-\dfrac{1}{1+e^{-t}}
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Newyork Nagaram...
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Thank you everyone!!! I got IT !!! Rep+ Everyone!
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