Results 1 to 2 of 2

Math Help - Differential equation and implicit mix- no idea

  1. #1
    Junior Member
    Joined
    May 2006
    Posts
    37

    Differential equation and implicit mix- no idea

    a. Two quantities x and y are related to each other by the differential equation ydy/dx=-16x. Solve this equation to get an implicit equation of the solution curve for which y=0 when x=0.1.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,707
    Thanks
    626
    Hello, kingkaisai2!

    This is the simplest type: Variables Separable . . .


    a. Two quantities x and y are related to each other
    . . by the differential equation: y\,\frac{dy}{dx} = -16x

    Solve this equation to get an implicit equation of the solution curve
    . . for which y=0 when x=0.1.

    We have: . y\,dy \:=\:16x\,dx

    Integrate: . \int y\,dy \:=\:\int 16x\,dx\quad\Rightarrow\quad \frac{1}{2}y^2\:=\:8x^2  + c\quad\Rightarrow\quad y^2\:=\:16x^2 + C

    When x = 0.1,\;y = 0:\;\;0^2 \:=\:16(0.1)^2 + C\quad\Rightarrow\quad C = -0.16

    Therefore: . \boxed{y^2\;=\;16x^2 - 0.16}

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: March 19th 2010, 08:06 PM
  2. No idea how to set up this equation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 19th 2009, 02:06 PM
  3. Replies: 1
    Last Post: July 30th 2009, 07:45 AM
  4. Replies: 6
    Last Post: April 24th 2009, 11:28 AM
  5. Differential equation in implicit form
    Posted in the Differential Equations Forum
    Replies: 8
    Last Post: March 16th 2009, 06:28 AM

Search Tags


/mathhelpforum @mathhelpforum