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**Omar Desoky****Guest**

Dears,

Answer each of the following:

(1) If y=x+1/x prove that x²(d²y/dx²)+x(dy/dx)=y

(2) Find the second derivative of (2x+3)/(3x-1) with respect ro (x-1)/(x+1)

(3) If y²=8/(1+x²) prove that (x²+1)(d²y/dx²)+3x(dy/dx)+y=0

(4) If y=(√x)+1/√x and z=(√x)-1/√x prove that d²y/dx²=(2x(y+2))/(x+1)³

(5) If y=cosx-3sinx prove that y'''+y''+y'+y=0

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,476

Hi;

Please read this:

http://www.mathisfunforum.com/viewtopic.php?id=14654

Please show a little bit of your work, or at least that you tried.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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Interesting, I will try

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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I can do 1, 4 and 5.

Please help with 2 and 3

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

**Online**

**Omar Desoky****Guest**

All is ok for me no problem about the final results but I only meed to make sure. of (2)

Thanls!

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,476

Hi Agnishom;

Let's do a simpler one so you can see the method.

Differentiate x^6 wrt x^2:

Say y = x^6, t =x^2

Now

Plugging in:

and that is the answer. There is an even simpler way involving a substitution.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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