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Math Help - Critical points and phase portraits

  1. #1
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    Critical points and phase portraits

    Find the critical points and phase portrait of the given autonomous first-order differential equation: dx/dt=x^2 - x^4. Classify each critical point as asymptotically stable, semi-stable, or unstable. Sketch the graph of a typical solution x(t) where x0 has the given values: (a) x0>1 (b) 0<x0<1 (c) -1<x0<0 (d) x0<-1.
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  2. #2
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    What did you get for x(t) ?
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  3. #3
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    I got (x∙ln(|x+1|)-x∙ln(|x-1|) - 2)/2x but couldn't figure out how to solve for x.
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  4. #4
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    Quote Originally Posted by kiddopop View Post
    I got (x∙ln(|x+1|)-x∙ln(|x-1|) - 2)/2x
    what is this equal to?
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  5. #5
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    (x∙ln(|x+1|)-x∙ln(|x-1|) - 2)/2x = t
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  6. #6
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    I understand. I was going about the problem in the completely wrong way.
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