Results 1 to 4 of 4
Like Tree2Thanks
  • 1 Post By TheEmptySet
  • 1 Post By JJacquelin

Math Help - Integrating y * dy/dt = x * dx/dt

  1. #1
    Member
    Joined
    Nov 2008
    Posts
    92

    Integrating y * dy/dt = x * dx/dt

    Hi,

    y(t) * dy(t)/dt = x(t) * dx(t)/dt

    My textbook says the integral is:

    y^2(t) - x^2(t) = constant.

    The part I'm not sure about is how they can put y(t) out of the integral sign, and just integrate dy(t)/dt, as y(t) is a function of time.

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78

    Re: Integrating y * dy/dt = x * dx/dt

    Quote Originally Posted by algorithm View Post
    Hi,

    y(t) * dy(t)/dt = x(t) * dx(t)/dt

    My textbook says the integral is:

    y^2(t) - x^2(t) = constant.

    The part I'm not sure about is how they can put y(t) out of the integral sign, and just integrate dy(t)/dt, as y(t) is a function of time.

    Thanks.
    My guess is that they are not.

    y\frac{dy}{dt}=x\frac{dx}{dt}

    With a little abuse of notation multiply both sides of the equation by dt

    ydy=xdx

    Now integrate both sides to get

    \int ydy = \int xdx  \implies \frac{1}{2}y^2=\frac{1}{2}x^2+c \iff y^2-x^2=\hat{c}
    Thanks from algorithm
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Aug 2011
    Posts
    243
    Thanks
    56

    Re: Integrating y * dy/dt = x * dx/dt

    y dy/dt = (1/2) d(y)/dt
    x dx/dt = (1/2) d(x)/dt
    y dy/dt = x dx/dt hence d(y)/dt = d(x)/dt
    Since the derivatives are equal, the functions differ only from a constant;
    y-x = c
    Thanks from algorithm
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Nov 2008
    Posts
    92

    Re: Integrating y * dy/dt = x * dx/dt

    I see. Thanks for your explanations.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Integrating 1/x^4
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 20th 2011, 03:17 AM
  2. Integrating (2x^2 -3)/x(x^2 +4
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 17th 2010, 06:14 AM
  3. Integrating pi x/2
    Posted in the Calculus Forum
    Replies: 8
    Last Post: April 20th 2009, 01:33 PM
  4. help with integrating this...
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 2nd 2008, 08:27 PM
  5. Integrating
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 25th 2008, 01:33 PM

Search Tags


/mathhelpforum @mathhelpforum