Results 1 to 5 of 5

Math Help - differental eq from calc

  1. #1
    Newbie
    Joined
    May 2009
    Posts
    10

    differental eq from calc

    if x=t^(2)+1 and y=t^3 than d^2y/dt^2=?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,963
    Thanks
    1784
    Awards
    1
    Quote Originally Posted by AnnaBee123 View Post
    if x=t^(2)+1 and y=t^3 than d^2y/dt^2=?
    Do you need \frac{d^2y}{dt^2} or \frac{d^2y}{dx^2}~?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by AnnaBee123 View Post
    if x=t^(2)+1 and y=t^3 than d^2y/dt^2=?

    well lets get started....

    \frac{dy}{dt}=3t^2

    Now if we take the derivative of the above with respect to t we get


    \frac{d}{dt}\left(\frac{dy}{dt} \right)=\frac{d}{dt}\left(3t^2 \right)

    \frac{d^2y}{dt^2}=6t
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    29
    Quote Originally Posted by Plato View Post
    Do you need \frac{d^2y}{dt^2} or \frac{d^2y}{dx^2}~?
    I was thinking the same as there was an equation given for both

    y=f(t) and x=f(t)

    Therefore a solution could be


    \frac{d^2y}{dx^2} = \frac{\tfrac{d^2y}{dt^2}}{\tfrac{d^2x}{dt^2}}

     = \frac{6t}{2}

     = 3t
    Last edited by pickslides; May 10th 2009 at 07:50 PM. Reason: typo
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by pickslides View Post
    I was thinking the same as there was an equation given for both

    y=f(t) and x=f(t)

    Therefore a solution could be


    \frac{d^2y}{dx^2} = \frac{\tfrac{d^2y}{dt^2}}{\tfrac{d^2x}{dt^2}}

     = \frac{6t}{2}

     = 3t
    We need to be careful...

    x=t^2+1 y=t^3

    so \frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}=  \frac{3t^2}{2t}=\frac{3}{2}t

    Now \frac{d^2y}{dx^2}=\frac{\frac{d}{dt}\frac{dy}{dx}}  {\frac{dx}{dt}}=\frac{\frac{3}{2}}{2t}=\frac{3}{4t  }

    Note we can write y as a function of x as follows

    y=(x-1)^{\frac{3}{2}}

    Now if we take two derivatives we get

    \frac{dy}{dx}=\frac{3}{2}(x-1)^{\frac{1}{2}}

    \frac{d^2y}{dx^2}=\frac{3}{4}\frac{1}{(x-1)^{\frac{1}{2}}}

    Note that since x=t^2+1 we get


    \frac{d^2y}{dx^2}=\frac{3}{4}\frac{1}{(x-1)^{\frac{1}{2}}}=\frac{3}{4}\frac{1}{(t^2+1-1)^{\frac{1}{2}}}=\frac{3}{4t}
    Last edited by TheEmptySet; May 10th 2009 at 09:37 PM. Reason: Missing 2
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. A few Pre-Calc problems in my AP Calc summer packet
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: August 30th 2010, 04:40 PM
  2. Strange Differental Equation Pls Help
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: January 13th 2010, 01:03 PM
  3. Replies: 1
    Last Post: January 13th 2010, 12:57 PM
  4. Ordinary Differental Equation
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: October 11th 2009, 03:09 PM
  5. What am I doing? Calc, Pre-calc, Trig, etc...
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: April 23rd 2008, 09:51 AM

Search Tags


/mathhelpforum @mathhelpforum