Results 1 to 6 of 6

Math Help - Solve Differential equation for the original equation

  1. #1
    Member
    Joined
    Feb 2009
    Posts
    118

    Solve Differential equation for the original equation

    Hi,

    Is my working correct for the following question?

    Question: Solve for the following differential equation for the original equation: \[<br />
 \frac{dy}{dx} = \frac{-x}{2y}<br />
\]

    Here is my working:

    \[<br />
 \frac{dy}{dx} = \frac{-x}{2y}<br />
\]

    \int2ydy = \int-xdx

    \frac{2y^2}{2} = \frac{-x^2}{2} + C

    Multiply both sides by 2:

    2y^2 = -x^2 + 2C

    What do I do next in order to solve the equation for the original equation?
    Last edited by sparky; February 21st 2011 at 12:57 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Well, you're pretty much done, aren't you? The only thing you could do is absorb the 2 into the C. If you want to solve for y, you could, I suppose. Make sure that when you take your square root, and you get two roots, that the ones you present as your solution actually satisfy the original DE.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Feb 2009
    Posts
    118
    Hi Ackbeet,

    On the teacher's answer sheet, I noticed he had the answer as

    X^2 + 2Y^2 = 0

    My question is, what happened to the C (or 2C)?

    If I bring everything except the C over, I get 2Y^2 + X^2 = 2C. How did he get 0?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    There's only one way to get C=0: you have an initial condition (which would have to be y(0)=0). Otherwise, you must have the C there.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Feb 2009
    Posts
    118
    Ok thanks Ackbeet!
    Follow Math Help Forum on Facebook and Google+

  6. #6
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    You're welcome. Have a good one!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help me solve this differential equation
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: December 19th 2010, 11:29 AM
  2. Cannot Solve this Differential Equation
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: February 17th 2010, 08:19 PM
  3. Replies: 13
    Last Post: May 19th 2008, 08:56 AM
  4. Solve Differential Equation
    Posted in the Calculus Forum
    Replies: 6
    Last Post: February 5th 2008, 06:22 PM
  5. Help solve a differential equation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 26th 2007, 01:19 AM

Search Tags


/mathhelpforum @mathhelpforum