Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    I was wondering if some one could check my answer here...currently working through Engineering Mathematics book. I am imposing the conditions I have two different ways, the latter I do not understand perhaps some guidance will be helpful.

    The question is ;

    Find the general solution of the equation

    y''+2y'+y=0

    Assume that y(0) = 3 and y'(0) = 1 to find particular solution.

    -----------------------------------------------------------------------------------


    Auxiliary equation m^{2}+2m-m=0

    Roots m= 1, \;\ m= -1

    So the general solution is y(x)=C_{1}e^{x}+C_{2}e^{-x} or y(x)=Ae^{x}+Be^{-x}

    Now to find the particular solution I impose the conditions

    y(0) = 3 gives 3 = A + B
    y'(0) = 1 gives 1 = 1A - 1B

    A + B = 3
    3A + 3B = 9
    -------------------
    -B = 12
    B = -12
    A - 12 = 3
    A = 3
    y_p(x)=3e^{x}- 12e^{-x} >>>>>>>>Final answer


    On the other hand if 3=C_{1}e^{1(0)}+C_{2}e^{-1(0)}\Rightarrow 3=C_{1}+C_{2}

    C_{2}=3-C_{1}

    Then for y' 1=1C_{1}e^{1(0)}+(3 - C_{1})e^{-1(0)}\Rightarrow 0=C_{1}-1

    Calculating with all this C_1, C_2 stuff is somewhat confusing, any advice? is my final answer correct?
    Offline

    13
    ReputationRep:
    Your auxiliary equation isn't correct. But your method is spot on. I think pluggin in the numbers you're given and finding simultaneous equations is fine, you just have to be careful that you have the right solutions.
    Offline

    18
    ReputationRep:
    Incorrect, surely?
    Offline

    13
    ReputationRep:
    Yah, my brain working faster than my hands syndrome :p:. Tend to forget to negate.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by insparato)
    Your auxiliary equation isn't correct. But your method is spot on. I think pluggin in the numbers you're given and finding simultaneous equations is fine, you just have to be careful that you have the right solutions.
    In this case the auxillary equation cant be consisting of a complex-conjugate....can it, because its greater >0 ?
    Offline

    13
    ReputationRep:
    y'' + 2y' + y = 0

    Auxiliary -> m^2 + 2m + 1 = 0

    Nope! Not complex.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by insparato)
    y'' + 2y' + y = 0

    Auxiliary -> m^2 + 2m + 1 = 0

    Nope! Not complex.
    doh! silly me thanks insparato.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: August 9, 2009
The home of Results and Clearing

1,237

people online now

1,567,000

students helped last year

University open days

  1. SAE Institute
    Animation, Audio, Film, Games, Music, Business, Web Further education
    Thu, 16 Aug '18
  2. Bournemouth University
    Clearing Open Day Undergraduate
    Fri, 17 Aug '18
  3. University of Bolton
    Undergraduate Open Day Undergraduate
    Fri, 17 Aug '18
Poll
Do you want your parents to be with you when you collect your A-level results?
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.