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Math Help - Equilibrium solutions to a D.E

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    Equilibrium solutions to a D.E

    hey all,

    How can I find remaining equilibrium solutions to \frac{dy}{dt} = -sin(x) + \frac{x}{2} ? The only solution I can find is 0.

    I see that it also touches the t-axis at approx -1.8 and 1.8, I guess I will just have to rely on the approximated values.
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    Quote Originally Posted by Oiler View Post
    hey all,

    How can I find remaining equilibrium solutions to \frac{dy}{dt} = -sin(x) + \frac{x}{2} ? The only solution I can find is 0.
    Are the x's meant to be y's ....? Are there boundary conditions? Note that by inspection sin(y) = y/2 for y = 0 but the other solutions cannot be found in closed form using algebra: solve Sin[x] = x/2 - Wolfram|Alpha
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    Quote Originally Posted by Oiler View Post
    hey all,

    How can I find remaining equilibrium solutions to \frac{dy}{dt} = -sin(x) + \frac{x}{2} ? The only solution I can find is 0.

    I see that it also touches the t-axis at approx -1.8 and 1.8, I guess I will just have to rely on the approximated values.
    There are actually three equilibrium points. x = 0 and x = +/- 1.562161 for y = const. See here.

    -Dan

    Aww! Beaten out by Elastic Man!
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