Results 1 to 8 of 8

Math Help - differential equations

  1. #1
    Newbie
    Joined
    May 2008
    Posts
    4

    differential equations

    Hello!

    this is my homework:

    y' = sin(1x)/2y

    can you help me please i'm in a hurry and have no idea how to solve this! I tried solving it like a homogenous DE but I didn't know how to transform DE into y/x form.

    sorry for my bad english

    regards, Vide

    EDIT: y' is derivate of y
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    As it's written, it's just a separable ODE.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2008
    Posts
    4
    ODE?
    If i want to solve it like a homogenous DE i need to transform SINx/2y in a
    y/x form so i can write u=y/x but i don't know how to transform it. Or is it DE of some other type, not homogenous?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    May 2008
    Posts
    4
    i tried basic separable metod and the result is (-cosx)^1/2 so i think that is homogenous DE.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by Vide View Post
    Hello!

    this is my homework:

    y' = sin(1x)/2y

    can you help me please i'm in a hurry and have no idea how to solve this! I tried solving it like a homogenous DE but I didn't know how to transform DE into y/x form.

    sorry for my bad english

    regards, Vide

    EDIT: y' is derivate of y
    \frac{dy}{dx}=\frac{\sin(x)}{2y}\Rightarrow{2ydy=\  sin(x)dx}

    integrating we get

    \int{2ydy}=y^2=\int\sin(x)dx=-\cos(x)+C

    solving for y we get

    y=\pm\sqrt{C-\cos(x)}
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    May 2008
    Posts
    4
    thanks! I forgot C now i see
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by Vide View Post
    thanks! I forgot C now i see
    Haha...yeah its ok...I have done that once or twice
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Chicago, IL
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by Mathstud28 View Post
    \frac{dy}{dx}=\frac{\sin(x)}{2y}\Rightarrow{2ydy=\  sin(x)dx}

    integrating we get

    \int{2ydy}=y^2=\int\sin(x)dx=-\cos(x)+C

    solving for y we get

    y=\pm\sqrt{C-\cos(x)}
    When solving a DE, we don't (well I don't) enjoy seeing \pm in the solution. Leaving it as the implicit solution y^2=C-\cos(x) would be more preferable. Your answer would be acceptable, given certain restricitions on y.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. 'Differential' in differential equations
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: October 5th 2010, 11:20 AM
  2. Replies: 2
    Last Post: May 18th 2009, 04:49 AM
  3. Differential Equations
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 12th 2009, 06:44 PM
  4. Replies: 5
    Last Post: July 16th 2007, 05:55 AM
  5. Replies: 3
    Last Post: July 9th 2007, 06:30 PM

Search Tags


/mathhelpforum @mathhelpforum