Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    been doing this question for 15 miin- to half and hour and its really starting to bug me - help!!!


    y=arsinh x, show that

    c) (1+x^2)f'''(x)+3x.f''(x)+f'x) = 0 - looks trivial, but its really long and cant get the LHS to equal teh zero after the differentiation and resubbing it

    (1+x^2) [f''(x)]^2 = 1 (this is given so use it

    pk
    Offline

    15
    ReputationRep:
    (Original post by Phil23)
    been doing this question for 15 miin- to half and hour and its really starting to bug me - help!!!


    y=arsinh x, show that

    c) (1+x^2)f'''(x)+3x.f''(x)+f'x) = 0 - looks trivial, but its really long and cant get the LHS to equal teh zero after the differentiation and resubbing it

    (1+x^2) [f''(x)]^2 = 1 (this is given so use it

    pk
    I think your hint is wrong - don't you mean

    (1+x^2) [f'(x)]^2 = 1

    If you differentiate this you get

    (1+x^2) 2 f' f'' + 2x (f')^2 = 0

    Divide by 2 f' =/= 0 to get

    (1+x^2) f'' + x f' = 0

    The differentiate this to get

    (1+x^2) f''' + 2x f'' + x f'' + f' = 0

    which is what you want
 
 
 
Turn on thread page Beta
Updated: June 18, 2005
The home of Results and Clearing

2,844

people online now

1,567,000

students helped last year

University open days

  1. Bournemouth University
    Clearing Open Day Undergraduate
    Wed, 22 Aug '18
  2. University of Buckingham
    Postgraduate Open Evening Postgraduate
    Thu, 23 Aug '18
  3. University of Glasgow
    All Subjects Undergraduate
    Tue, 28 Aug '18
Poll
How are you feeling about GCSE results day?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.