General solution to dy/dx = ky

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

Announcements Posted on
Please change your TSR password 23-05-2013
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. jsmith6131's Avatar
    1 10-04-2012  18:08
    • Overlord in Training
    General solution to dy/dx = ky
    I am trying to prove that the general solution to
    \frac {dy}{dx} = ky

    y=Ce^k^x

    Here is my working
    \frac {1}{ky} dy = dx

    \int (ky)^-^1 dy = \int dx

    \frac {ln y}{k} = x + c

    lny = k(x + c)

    y = e^k^(^x^+^c^)

    y=e^k^xe^k^c

    How to I prove the equation?
  2. SpongebobSquarepan's Avatar
    2 10-04-2012  18:10
    • Exalted Member
    • Posts: 377
    Re: General solution to dy/dx = ky
    1/y dy = k dx

    lny = kx + c
    y = exp^kx+c
    y = Cexp^kx

    You owe me £50
  3. jsmith6131's Avatar
    3 10-04-2012  18:17
    • Overlord in Training
    Re: General solution to dy/dx = ky
    (Original post by SpongebobSquarepan)
    1/y dy = k dx

    lny = kx + c
    y = exp^kx+c
    y = Cexp^kx

    You owe me £50
    of course kc = constant * constant = another constant

    thanks

    there we go, £50:
  4. TenOfThem's Avatar
    4 10-04-2012  18:19
    • TSR Royalty
    Re: General solution to dy/dx = ky
    (Original post by jsmith6131)


    y=e^k^xe^k^c

    How to I prove the equation?
    You say let C = e^{kc}
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.