Hi All,

Given and

then u"(x) is calculated as

How was this derived?

I calculate both u'(x) and u"(x) to be equal to Ae^x. I dont know how the A^2 appears in front of u(x)!!!.....

Thanks

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- Dec 2nd 2010, 09:38 PMbugatti792nd order differentiation query
Hi All,

Given and

then u"(x) is calculated as

How was this derived?

I calculate both u'(x) and u"(x) to be equal to Ae^x. I dont know how the A^2 appears in front of u(x)!!!.....

Thanks - Dec 3rd 2010, 04:30 AMHallsofIvy
Why do you say that "is calculated as ? If then and . That can be written as if and only if so that .

- Dec 3rd 2010, 06:52 AMbugatti79
My lecture notes reads

therefore

????

Therefore implies

I dont understand the third line!!...I dont think its the standard way of getting solution for a nd order equation?

Thanks - Dec 3rd 2010, 07:05 AMhmmmm
so you have and ?? In the third line, that seems strange?

- Dec 3rd 2010, 09:16 AMbugatti79
I dont know what his method is. I think I will just stick with the standard way of getting the solution ie,

is of the form

giving roots

therefore

therefore solution is

This ok? - Dec 4th 2010, 04:24 AMHallsofIvy
[QUOTE=bugatti79;591430]My lecture notes reads

therefore

[/quote

This is wrong. If then**not**.

Quote:

????

Therefore implies

I dont understand the third line!!...I dont think its the standard way of getting solution for a nd order equation?

Thanks

If , then so . - Dec 4th 2010, 12:13 PMbugatti79
aha, thats what it was. It mustve been a typo on behalf or the lecturers :-)

But the standard derivation in post 5is correct? Thanks - Dec 5th 2010, 04:29 AMHallsofIvy
Why did you change from k to n? If the differential equation is , then the characteristic equation is so that and the general solution to the differential equation is . Note that this could also be written as .

By the way, using two consecutive**single quotes**in LaTex rather than a double quote will give rather than . - Dec 5th 2010, 10:46 AMbugatti79