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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: 7,613

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

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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: 7,613

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

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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: 7,613

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

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