Differential equation question.

Can anyone illustrate the method for how to do this question.

Reputation points to any person who can show me a fully worked solution.

Cheers


Posted from TSR Mobile

You start with Sin(y) = x

You differentiate

You spot that Cos(y) = the root of (1-sin^2x)



I could give you a fully worked answer so I expect the Rep points in spite of the fact that I will not since I think you will learn more if you think it through yourself

You start with Sin(y) = x

You differentiate

You spot that Cos(y) = the root of (1-sin^2x)



I could give you a fully worked answer so I expect the Rep points in spite of the fact that I will not since I think you will learn more if you think it through yourself

Hi,

i can do all of that bit my friend. I can get up to the bit where we show that y=ksin-1x satisfies the differential equation.
It is the bit beyond (in other word beyond the "in this particular case" part) that i cannot do despite struggling for hours.
I too also agree with your sentiment in your reply; however I have exhausted all options on this question, and tsr has been my last resort. Please could you show me how to do this question ...... so that I can work backwards. Sometimes one can learn more working backwards than they did working forwards if you know what i mean.


P. s this isn't coursework or homework- rather independent study/revision.

Judging by the question style and content... this is STEP III question?

If so, you really should be spending at least 2 days on the question before seeking any guidance.

Can you elaborate a bit more/actually show me.
The best way to show me would be for you to do the worked solution on a piece of paper and then take a photo of your working. It's pretty easy to do in the mobile phone if you the tsr app

Judging by the question style and content... this is STEP III question?

If so, you really should be spending at least 2 days on the question before seeking any guidance.

Since you asked:



Apologies for the lack of clarity (hastily writing it down as well as a rubbish phone camera ). The first image contains the first part (with the second bit at the top right corner), and the second image contains the bit which you were asking about (the last part).

EDIT:

I put the solution in latex because it's better like that:

It's almost, but not quite, identical to STEP I 1999 Q7

Hmmm. thanks for pointing this out. Is my above post a step paper question as well?

My friends on TSR.

Due to the success of the last solution of my last problems could you guys help me out with another tricky question please. In the same manner as before (a worked solution).



Once again. Working backwards is much more fruitful IMO sometimes than working forwards
rep points to anyone who helps

Posted from TSR Mobile

I don't recognize it, but then I only recognized the last one because I remembered doing it a couple of months ago!



That's not really how TSR works! You should have a go at this question and post your working when you get stuck so that someone can help you move forwards. How far have you got with this particular question?

Can do the first 1/3. But no further. And tsr needs to understand that not all people learn the same way.

I understand your sentiment but i must stress i have tried this question and reached a brick wall. Hence, why i am on tsr.

..

Desperation is not an attractive quality.

Show your working. TSR is not a homework service.

this isn't homework .

Of course it isn't.

So I imagine the bit you can't do is to derive the reduction formula.

$\displaystyle I_n = \int_1^e x (\ln x)^n \, dx$

Integrate by parts.

$\displaystyle I_n = \left[ \frac{x^2 (\ln x)^n}{2} \right]_1^e - \frac{n}{2} \int_1^e x (\ln x)^{(n-1)} \, dx$