Turn on thread page Beta
    • Thread Starter
    Offline

    4
    ReputationRep:
    Hi,

    I can't seem to get the correct answer when solving this differential equation:

    4d²y/dx² - 4dy/dx + 5y = 0

    as the answer is e^(1/2x)[Acosx+Bsinx], although I am getting
    e^x[Acos(x/2)+Bsin(x/2)]

    Can someone please help?

    Thanks!
    Offline

    13
    ReputationRep:
    Hmm shouldnt give out full answers.

    Could you provide us with your workings out?
    • Thread Starter
    Offline

    4
    ReputationRep:
    4d²y/dx² - 4dy/dx + 5y = 0

    Auxiliary equation:

    4m²-4m+5=0
    (2m-2)²-4+5=0
    (2m-2)²=-1
    2m-2=±i
    m=1±(1/2)i

    therefore, the general solution is:

    y=Pe^[1+(1/2)i]x + Qe^[1-(1/2)i]x
    y=e^x{Pe^[(1/2)ix] + Qe^[(-1/2)ix]}
    y=e^x(Acos[(1/2)x] + Bcos[(1/2)x]) where A=P+Q and B=i(P-Q)
    Offline

    13
    ReputationRep:
    Now that is weird. I used the quadratic equation for this question.

     \tex \large x = \frac{4\pm\sqrt{16 - 4 x 4 x 5}}{8} = \frac{4\pm\sqrt{-64}}{8} = \frac{4\pm8i}{8} = \frac{1}{2} \pm i

    That will give you the right answer.

    However i dont understand why completing the square didnt work :confused:.
    Offline

    2
    ReputationRep:
    4m² - 4m + 5 = 0
    (2m - 2)² - 4 + 5 = 0

    Checking this...

    (2m - 2)(2m - 2) - 4 + 5 = 0
    4m^2 - 4m - 4m + 4 - 4 + 5 = 0
    4m^2 - 8m + 5 = 0

    Not what you wanted.
    Offline

    13
    ReputationRep:
    aahhhh damn should've seen that.
    • Thread Starter
    Offline

    4
    ReputationRep:
    Ohh I see, I've completed the square wrong! I'll have a go at that again, thanks for your help everyone!
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: October 14, 2006

University open days

  • University of Bradford
    All faculties Undergraduate
    Wed, 21 Nov '18
  • Buckinghamshire New University
    All Faculties Postgraduate
    Wed, 21 Nov '18
  • Heriot-Watt University
    All Schools Postgraduate
    Wed, 21 Nov '18
Poll
Black Friday: Yay or Nay?
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

Equations

Best calculators for A level Maths

Tips on which model to get

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.