Turn on thread page Beta

Solving ODE's with the method of variation of paramaters and reduction of order watch

    • Thread Starter
    Offline

    13
    ReputationRep:
    hello, i was just wondering if anyone could help me with the following problem.

    Name:  variaton.png
Views: 42
Size:  7.5 KB i calculated the wronskian as e^-4x and the general solution i obtained was y=c1e^-2x+c2xe^-2x-x+ln|x| but i'm not sure it is correct, any help would be appreciated
    Offline

    22
    ReputationRep:
    (Original post by Scary)
    hello, i was just wondering if anyone could help me with the following problem.

    Name:  variaton.png
Views: 42
Size:  7.5 KB i calculated the wronskian as e^-4x and the general solution i obtained was y=c1e^-2x+c2xe^-2x-x+ln|x| but i'm not sure it is correct, any help would be appreciated
    Post a picture of your working, looks like you made a small slip somewhere.
    • Thread Starter
    Offline

    13
    ReputationRep:
    (Original post by Zacken)
    Post a picture of your working, looks like you made a small slip somewhere.
    Name:  image.jpg
Views: 40
Size:  441.6 KB Excuse my atrocious handwriting
    Offline

    14
    ReputationRep:
    (Original post by Scary)
    Excuse my atrocious handwriting
    Yes, just a small slip - you've factored the characteristic equation incorrectly.

     \displaystyle m^2 - 4m + 4 = (m -2)^2

    The wronskian will come out as e^{4x}
    • Thread Starter
    Offline

    13
    ReputationRep:
    (Original post by Gregorius)
    Yes, just a small slip - you've factored the characteristic equation incorrectly.

     \displaystyle m^2 - 4m + 4 = (m -2)^2

    The wronskian will come out as e^{4x}
    Ahh thank you!
    • Thread Starter
    Offline

    13
    ReputationRep:
    So the final solution I acquired was y=Ae^2x+Bxe^2x+xe^2x(ln|x|-1) I'm just wondering when doing the intergration to calculate the particular integral should one include the constants of integration with the formula which you would use to generate this
    • Thread Starter
    Offline

    13
    ReputationRep:
    bump
 
 
 
The home of Results and Clearing

3,454

people online now

1,567,000

students helped last year

University open days

  1. Bournemouth University
    Clearing Open Day Undergraduate
    Fri, 17 Aug '18
  2. University of Bolton
    Undergraduate Open Day Undergraduate
    Fri, 17 Aug '18
  3. Bishop Grosseteste University
    All Courses Undergraduate
    Fri, 17 Aug '18
Poll
Will you be tempted to trade up and get out of your firm offer on 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.