Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    I[y]=\int_a^b y'^2 + y^4 dx .

    The Euler lagrange equation of this functional yields the D.E.

    y'' = 2y^3 How do I solve this?!

    I tried differentiating both sides and letting z=y' but that doesn't really get me anywhere. any ideas..
    Offline

    4
    ReputationRep:
    z = y' is the right direction. See if you can't use the chain rule somehow
    Offline

    2
    ReputationRep:
    Multiply both sides by 2y`
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by matt2k8)
    Multiply both sides by 2y`
    I actually did that but that ultimately gives me:

    y'^2 = y^4 + C and unless C=0 which I can't see any way of showing I cannot solve that .

    Edit: btw, I am given y(a) = y(b) = 0

    I am guessing actually that the solution is simply y= 0! as that minimises the functional!
    Offline

    2
    ReputationRep:
    Going by what Wolfram Alpha says, it seems the solution doesn't have an expression in terms of elementary functions...
    Offline

    4
    ReputationRep:
    I assume the initial conditions are y(a) = y'(a) = 0 to make C = 0 which then lets you finish up.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: September 26, 2010
Poll
Do I go to The Streets tomorrow night?
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.