Results 1 to 3 of 3

Math Help - solve the differential equation

  1. #1
    Member
    Joined
    Dec 2008
    From
    Australia
    Posts
    161

    Cool solve the differential equation

    Solve the differential equation dy/dx= 2y for y given that when x = 1, y = 1

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    1. separate the variables

    dy/y = 2dx

    2. integrate

    ln|y| = 2x+ c

    3. Apply ICs x= y = 1

    0 = 2 + c

    c=-2

    ln|y| = 2x - 2

    4. exponentiate

    y = e^(2x-2) = e^(-2) e^(2x)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,653
    Thanks
    1478
    Quote Originally Posted by differentiate View Post
    Solve the differential equation dy/dx= 2y for y given that when x = 1, y = 1

    Thanks
    \frac{dy}{dx} = 2y


    Method 1:

    \frac{dx}{dy} = \frac{1}{2y}

    x = \int{\frac{1}{2y}\,dy}

    x = \frac{1}{2}\ln{|y|} + c

    x - c = \frac{1}{2}\ln{|y|}

    2x - C = \ln{|y|} where C = 2c

    |y| = e^{2x - C}

    |y| = e^{-C} e^{2x}

    y = \pm e^{-C} e^{2x}

    y = A e^{2x} where A = \pm e^{-C}.


    Now letting x = 1, y = 1 we find

    1 = Ae^{2(1)}

    1 = Ae^2

    A = e^{-2}.


    So y = e^{-2} e^{2x}

    y = e^{2x - 2}.



    Other possible methods are separation of variables or integrating factor.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Solve Differential equation for the original equation
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: February 21st 2011, 01:24 PM
  2. Solve a Differential Equation
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: January 12th 2010, 05:55 AM
  3. solve the following differential equation
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: April 11th 2009, 04:56 AM
  4. solve differential equation HELP pls
    Posted in the Differential Equations Forum
    Replies: 9
    Last Post: March 8th 2009, 01:51 PM
  5. Replies: 13
    Last Post: May 19th 2008, 08:56 AM

Search Tags


/mathhelpforum @mathhelpforum