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Homework Help: Plotting isoclines corresponding to slopes m = +1 and m -1?

  1. Aug 21, 2013 #1
    Given the first order ODE y' = 2 * y^3 * x, plot the isoclines corresponding to slopes m = +1 and m = -1.

    My answer:

    The isoclines are given by m= 2 * y^3 * x or y=(m/(2*x))^1/3

    The slope elements on the isocline y=+- (m/(2*x))^1/3 all have gradient m

    For m = 1, the isocline is y = +- (1/(2*x))^1/3
    For m = -1, the isocline is y = +- (-1/(2*x))^1/3

    and hence l simply plotted the above two equations

    Can anyone confirm whether or not l am correct

    Thanks
     
  2. jcsd
  3. Aug 21, 2013 #2
    Seems correct except in
    You don't need [itex]\pm[/itex] because you're taking the cube root not the square root.
     
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