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anonymous

  • one year ago

The general solution of the differential equation dy − 0.2x dx = 0 is a family of curves. These curves are all lines hyperbolas parabolas ellipses

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  1. anonymous
    • one year ago
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    http://www.wolframalpha.com/widgets/view.jsp?id=e602dcdecb1843943960b5197efd3f2a

  2. anonymous
    • one year ago
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    i'm thinking hyperbolas but not sure

  3. anonymous
    • one year ago
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    \[dy=0.2x dx\] by moving over \[\int\limits dy=\int\limits 0.2x dx\] Is that what you did?

  4. anonymous
    • one year ago
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    and then I got y=0.2 which is a graph of a straight line at y=0.2, so I would call it a line.

  5. anonymous
    • one year ago
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    um .. no i just shamelessly plugged it into wolfram :P

  6. anonymous
    • one year ago
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    Does this involve the slope field?

  7. anonymous
    • one year ago
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    it might, some of the other questions iv been asked have involved the slope field

  8. anonymous
    • one year ago
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    plug the equation into wolfram and scroll down to the family curve , it seems to show a parabola or hyperbola

  9. Michele_Laino
    • one year ago
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    after a simple integration I got this: \[\Large \int {dy = 0.2\int {xdx} = 0.2 \cdot \frac{{{x^2}}}{2}} + C\]

  10. anonymous
    • one year ago
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    Seems like a parabola. Any 2 curves symmetrical is a hyperbola.

  11. anonymous
    • one year ago
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    oh yea. I took derivative instead of integrating it..

  12. anonymous
    • one year ago
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    okay can you just explain to me what the hell family curves are ?

  13. Michele_Laino
    • one year ago
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    since C is an arbitrary real constant, whose values can vary inside the set of real numbers, in other words, we have: \[\Large C \in \mathbb{R}\]

  14. Michele_Laino
    • one year ago
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    |dw:1439275918663:dw|

  15. anonymous
    • one year ago
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    Family curves are a set of curves. If the function C is a constant value added to all the family curves, that means all of the curves have the same behavior right?

  16. anonymous
    • one year ago
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    oh okay so basically its what the graph would look like despite what c could be, right?

  17. Michele_Laino
    • one year ago
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    yes! right! they differ only for the value of C

  18. anonymous
    • one year ago
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    If the function y C* I mean.

  19. anonymous
    • one year ago
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    okay and this graph would look like a parabola despite what c is right?

  20. anonymous
    • one year ago
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    Since the graph shows the curves not symmetrical, therefore it cannot be a parabola.

  21. anonymous
    • one year ago
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    I mean it cannot be a hyperbola.

  22. Michele_Laino
    • one year ago
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    right! @Jdosio

  23. anonymous
    • one year ago
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    okay thank you guys very much :D

  24. Michele_Laino
    • one year ago
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    :)

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