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#1 2012-09-26 14:50:12
- Graeme92
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- Registered: 2012-09-25
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second derivative
Find the analytic solution for this equation in terms of two constants by integrating twice.
d²h/dx² = -R/K = 2 x 10-5
h(0) = 1000 ; h(10000) = 1000
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#2 2012-09-26 14:53:53
- Graeme92
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- Registered: 2012-09-25
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Re: second derivative
2nd order differential equation
Find the analytic solution for this equation in terms of two constants by integrating twice.
d/dx(h * dh/dx) = 0
h(0) = 40 ; h(10000) = 40
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#3 2012-09-26 19:01:39
- Bob
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- Registered: 2010-06-20
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Re: second derivative
hi Graeme92
Welcome to the forum.
If N is a number
Then you can substitute in the given values to determine C and D.
The second question starts the same but you might be wondering what to do with
where F is the function after the first integration.
You can think of this as
Post again if you need more detail.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob 
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#4 2012-09-27 02:21:59
- Graeme92
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- Registered: 2012-09-25
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Re: second derivative
Thank you for this, Bob. Can you give me a reference for the second question, and I am not sure about "F".
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#5 2012-09-27 04:16:08
- Bob
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Re: second derivative
hi Graeme92
Actually all integration is like question 2!
eg.
Splitting the derivative like this is used a lot in differential equations.
You only need to introduce a constant of integration on one side as a constant on each side could be replaced by just one.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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#6 2012-09-27 12:01:10
- Graeme92
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- Registered: 2012-09-25
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Re: second derivative
Thanks again Bob, but how do you solve for h?
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#7 2012-09-27 18:39:20
- Bob
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- Registered: 2010-06-20
- Posts: 10,648
Re: second derivative
hi Graeme92
You've been given enough information to substitute in and work out the constants, C and D. So the 'solution' will be a formula for calculating h, given any value for x.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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