Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    2
    ReputationRep:
    Find the general solution of the differential equation
     \displaystyle 4xy'' + 4x(y')^2+2y' -1= 0 .

    It could be difficult right?
    • Thread Starter
    Offline

    2
    ReputationRep:
    Why is no one helping me? 81 views and still no one.
    Is it too hard?
    Offline

    17
    ReputationRep:
    Define u(x) s.t. u'=uy', then note that:

     u'' = u'y' + uy'' \Rightarrow 4xy''+ \underbrace{4x\frac{u'^2}{u^2}}_  {4xy'^2} =\dfrac{4xu''}{u} ,

    Which reduces our non-linear ODE to the more reasonable second order ODE:

    4xu'' +2u' - u=0.
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by Farhan.Hanif93)
    Define u(x) s.t. u'=uy', then note that:

     u'' = u'y' + uy'' \Rightarrow 4xy''+ \underbrace{4x\frac{u'^2}{u^2}}_  {4xy'^2} =\dfrac{4xu''}{u} ,

    Which reduces our non-linear ODE to the more reasonable second order ODE:

    4xu'' +2u' - u=0.
    Then what you gonna do from there though?
    Offline

    17
    ReputationRep:
    (Original post by Ano123)
    Then what you gonna do from there though?
    You're asking the wrong question - the question is: what are you going to do from here? The ODE is not too difficult at all from this point; if you want more help, post your working.

    If you're looking for a hint: Can you spot a substitution that simplifies this?
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by Farhan.Hanif93)
    You're asking the wrong question - the question is: what are you going to do from here? The ODE is not too difficult at all from this point; if you want more help, post your working.

    If you're looking for a hint: Can you spot a substitution that simplifies this?
    I've already got the answer doing it a different way - I don't need help. Seeing how others do it.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Would you like to hibernate through the winter months?
    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
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • 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

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