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Math Help - first order autonomous eq

  1. #1
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    first order autonomous eq

    Hello
    I have a question so if someone can help me:

    Solve the autonmous problem
    dx/dt= y,
    dy/dt= 4x
    by viewing y as a function of x with dy/dx=4x/y
    inital conditions:
    x(0) = 1, y(0) = 10

    Thanks in advance
    Jewons
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  2. #2
    MHF Contributor

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    Quote Originally Posted by jewons View Post
    Hello
    I have a question so if someone can help me:

    Solve the autonmous problem
    dx/dt= y,
    dy/dt= 4x
    by viewing y as a function of x with dy/dx=4x/y
    inital conditions:
    x(0) = 1, y(0) = 10

    Thanks in advance
    Jewons
    Well, dy/dx= 4x/y is separable, isn't it? Integrate both sides of ydy= 4xdx and then use the fact that y= 10 when x= 0 to determine the constant of integration.
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  3. #3
    Newbie
    Joined
    May 2010
    Posts
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    hello

    I have tried to do that and I have some algebraic problem then
    What I get when integrate bothe parts is y^2/2=4x^2/2 +c
    or y^2=4x2+c but I do not know how to proceed than?
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