Results 1 to 4 of 4

Math Help - ODE question!

  1. #1
    Junior Member
    Joined
    Nov 2008
    Posts
    53

    ODE question!

    The following equation arises in the mathematical modeling of reverse osmosis.
    (sin t)y'' - 2(cos t)y' - (sin t)y = 0, 0 < t < pi

    Find a general solution. Hint: First observe that y = cos t is as solution, but the sine function is not a solution. To find a second solution, apply the reduction of order technique.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by ninano1205 View Post
    The following equation arises in the mathematical modeling of reverse osmosis.
    (sin t)y'' - 2(cos t)y' - (sin t)y = 0, 0 < t < pi

    Find a general solution. Hint: First observe that y = cos t is as solution, but the sine function is not a solution. To find a second solution, apply the reduction of order technique.
    treat y = v(t) \cos t as the second solution.

    now solve for v(t) by treating the above as a particular solution

    can you finish?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Nov 2008
    Posts
    53

    Thank you for reply but,

    I can't understand what u meant by saying by treating the above as a particular solution?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Jhevon View Post
    treat y = v(t) \cos t as the second solution.

    now solve for v(t) by treating the above as a particular solution

    can you finish?
    Quote Originally Posted by ninano1205 View Post
    I can't understand what u meant by saying by treating the above as a particular solution?
    It's fair to assume you've been taught this technique so it should be clear what's meant.

    Substitute y = v \cos t into the DE. This will give you (after simplifying) a new DE with v in it. Solve this DE for v.
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum