Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**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: 96,585

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.**

**If it ain't broke, fix it until it is.**

**Online**

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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

Offline

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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

Offline

**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: 96,585

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.**

**If it ain't broke, fix it until it is.**

**Online**