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## #1 2012-09-27 12:50:12

Graeme92
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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

## #2 2012-09-27 12:53:53

Graeme92
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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

## #3 2012-09-27 17:01:39

bob bundy
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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

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

## #4 2012-09-28 00:21:59

Graeme92
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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".

## #5 2012-09-28 02:16:08

bob bundy
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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

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

## #6 2012-09-28 10:01:10

Graeme92
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### Re: second derivative

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

## #7 2012-09-28 16:39:20

bob bundy
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### 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

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

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