MEI C4 Differential Equations

Maths and statistics discussion, revision, exam and homework help.

Announcements Posted on
Enter our travel-writing competition for the chance to win a Nikon 1 J3 camera 21-05-2013
IMPORTANT: You must wait until midnight (morning exams)/4.30AM (afternoon exams) to discuss Edexcel exams and until 1pm/6pm the following day for STEP and IB exams. Please read before posting, including for rules for practical and oral exams. 28-04-2013
Search Thread
Advanced Search
Sign in to Reply
  1. Hippysnake's Avatar
    1 18-04-2010  21:18
    • TSR Demigod
    • Location: Moon
    MEI C4 Differential Equations
    Obtain a particular solution to (1-e^2y)dy/dx = e^y

    Given that y=1 when x=2.
    There is no need to express y in terms of x.

    Any ideas?
  2. Pheylan's Avatar
    2 18-04-2010  21:22
    • Banned
    • Warning points: 1000
    Re: MEI C4 Differential Equations
    \frac{1-e^{2y}}{e^y}dy=dx

    e^{-y}-e^ydy=dx

    \int e^{-y}-e^y\ dy=\int 1\ dx

    -e^{-y}-e^y=x+C
  3. ziedj's Avatar
    3 18-04-2010  21:29
    • Overlord in Training
    • Posts: 2,003
    Re: MEI C4 Differential Equations
    (Original post by Pheylan)
    \frac{1-e^{2y}}{e^y}dy=dx

    e^{-y}-e^ydy=dx

    \int e^{-y}-e^y\ dy=\int 1\ dx

    -e^{-y}-e^y=x+C
    carry on..
  4. Pheylan's Avatar
    4 18-04-2010  21:33
    • Banned
    • Warning points: 1000
    Re: MEI C4 Differential Equations
    (Original post by ziedj)
    carry on..
    -e^{-1}-e^1=2+C

    C=-(e+\frac{1}{e}+2)

    -e^{-y}-e^y=x-(e+\frac{1}{e}+2)

    e+\frac{1}{e}+2=x+e^y+\frac{1}{e ^y}
  5. ziedj's Avatar
    5 18-04-2010  21:34
    • Overlord in Training
    • Posts: 2,003
    Re: MEI C4 Differential Equations
    (Original post by Pheylan)
    -e^{-1}-e^1=2+C

    C=-(e+\frac{1}{e}+2)

    -e^{-y}-e^y=x-(e+\frac{1}{e}+2)

    e+\frac{1}{e}+2=x+e^y+\frac{1}{e ^y}
    You have passed the test. One internet will be sent your way.
  6. time.to.dance's Avatar
    6 18-04-2010  21:36
    • Exalted and Worshipped Member
    • Location: London
    • Posts: 1,178
    Re: MEI C4 Differential Equations
    Solved the solution up to substituting the x and y values and was about to post when i scrolled down and saw Pheylan's answer :sigh:
  7. Hippysnake's Avatar
    7 18-04-2010  21:36
    • TSR Demigod
    • Location: Moon
    Re: MEI C4 Differential Equations
    (Original post by Pheylan)
    \frac{1-e^{2y}}{e^y}dy=dx

    e^{-y}-e^ydy=dx

    \int e^{-y}-e^y\ dy=\int 1\ dx

    -e^{-y}-e^y=x+C
    so is x + e^-y + e^y = 4 the particular solution?
  8. Pheylan's Avatar
    8 18-04-2010  21:38
    • Banned
    • Warning points: 1000
    Re: MEI C4 Differential Equations
    (Original post by Hippysnake)
    so is x + e^-y + e^y = 4 the particular solution?
    this is:
    (Original post by Pheylan)
    -e^{-1}-e^1=2+C

    C=-(e+\frac{1}{e}+2)

    -e^{-y}-e^y=x-(e+\frac{1}{e}+2)

    e+\frac{1}{e}+2=x+e^y+\frac{1}{e ^y}
  9. ziedj's Avatar
    9 18-04-2010  21:38
    • Overlord in Training
    • Posts: 2,003
    Re: MEI C4 Differential Equations
    (Original post by Hippysnake)
    so is x + e^-y + e^y = 4 the particular solution?
    where did 4 come from?
  10. Pheylan's Avatar
    10 18-04-2010  21:39
    • Banned
    • Warning points: 1000
    Re: MEI C4 Differential Equations
    (Original post by time.to.dance)
    Solved the solution up to substituting the x and y values and was about to post when i scrolled down and saw Pheylan's answer :sigh:
    sorry :awesome:
  11. Hippysnake's Avatar
    11 18-04-2010  21:44
    • TSR Demigod
    • Location: Moon
    Re: MEI C4 Differential Equations
    Cheers dude. How about this one?

    x^2 dy/dx - y^2 =0?

    I end up with y = x + c but that seems a bit too easy...
  12. Pheylan's Avatar
    12 18-04-2010  21:49
    • Banned
    • Warning points: 1000
    Re: MEI C4 Differential Equations
    \frac{dy}{dx}=\frac{y^2}{x^2}

    y^{-2}dy=x^{-2}dx

    \int y^{-2}\ dy=\int x^{-2}\ dx

    -y^{-1}=-x^{-1}+C

    -\frac{1}{y}=-\frac{1}{x}+C

    -x=-y+Cxy

    y=x+Cxy
  13. Hippysnake's Avatar
    13 18-04-2010  21:55
    • TSR Demigod
    • Location: Moon
    Re: MEI C4 Differential Equations
    (Original post by Pheylan)
    \frac{dy}{dx}=\frac{y^2}{x^2}

    y^{-2}dy=x^{-2}dx

    \int y^{-2}\ dy=\int x^{-2}\ dx

    -y^{-1}=-x^{-1}+C

    -\frac{1}{y}=-\frac{1}{x}+C

    -x=-y+Cxy

    y=x+Cxy
    I got x/1+cx?

    Ah well, I have one more question?

    At time t seconds the rate of increase in the concentration of flesh eating bugs in a controlled environment is proportional to the concentration C of bugs present. Initially C= 100 bugs and after 2 seconds there are five times as many.

    Write down a differential equation connection dC/dt, C and t and hence find an expression for C in terms of t.
Sign in to Reply
Search Thread
Advanced Search
Share this discussion:  
Useful resources

Articles:

Study Help rules and posting guidelinesStudy Help Member of the Month nominationsGuide to MathematicsMathematics resourcesMathematics websitesMathematics revision notes in the TSR wikiCambridge Assessment admissions tests (including STEP)How to use LaTeXCareers in Mathematics

Useful Dates:

Quick Link:

Unanswered Maths Threads

Groups associated with this forum:

View associated groups
Article updates
Moderators

We have a brilliant team of more than 60 volunteers looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is moderated by:

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

Shortcuts

Get Started

TSR Group

Using TSR

Info

Connect with TSR

Reputation gems:
The Reputation gems seen here indicate how well reputed the user is, red gem indicate negative reputation and green indicates a good rep.
Post rating score:
These scores show if a post has been positively or negatively rated by our members.