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**Graeme92****Member**- Registered: 2012-09-25
- Posts: 4

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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**Graeme92****Member**- Registered: 2012-09-25
- Posts: 4

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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,654

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

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**Graeme92****Member**- Registered: 2012-09-25
- Posts: 4

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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,654

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

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**Graeme92****Member**- Registered: 2012-09-25
- Posts: 4

Thanks again Bob, but how do you solve for h?

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,654

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

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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