anonymous
  • anonymous
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
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
http://www.wolframalpha.com/widgets/view.jsp?id=e602dcdecb1843943960b5197efd3f2a
anonymous
  • anonymous
i'm thinking hyperbolas but not sure
anonymous
  • anonymous
\[dy=0.2x dx\] by moving over \[\int\limits dy=\int\limits 0.2x dx\] Is that what you did?

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anonymous
  • anonymous
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.
anonymous
  • anonymous
um .. no i just shamelessly plugged it into wolfram :P
anonymous
  • anonymous
Does this involve the slope field?
anonymous
  • anonymous
it might, some of the other questions iv been asked have involved the slope field
anonymous
  • anonymous
plug the equation into wolfram and scroll down to the family curve , it seems to show a parabola or hyperbola
Michele_Laino
  • Michele_Laino
after a simple integration I got this: \[\Large \int {dy = 0.2\int {xdx} = 0.2 \cdot \frac{{{x^2}}}{2}} + C\]
anonymous
  • anonymous
Seems like a parabola. Any 2 curves symmetrical is a hyperbola.
anonymous
  • anonymous
oh yea. I took derivative instead of integrating it..
anonymous
  • anonymous
okay can you just explain to me what the hell family curves are ?
Michele_Laino
  • Michele_Laino
since C is an arbitrary real constant, whose values can vary inside the set of real numbers, in other words, we have: \[\Large C \in \mathbb{R}\]
Michele_Laino
  • Michele_Laino
|dw:1439275918663:dw|
anonymous
  • anonymous
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?
anonymous
  • anonymous
oh okay so basically its what the graph would look like despite what c could be, right?
Michele_Laino
  • Michele_Laino
yes! right! they differ only for the value of C
anonymous
  • anonymous
If the function y C* I mean.
anonymous
  • anonymous
okay and this graph would look like a parabola despite what c is right?
anonymous
  • anonymous
Since the graph shows the curves not symmetrical, therefore it cannot be a parabola.
anonymous
  • anonymous
I mean it cannot be a hyperbola.
Michele_Laino
  • Michele_Laino
right! @Jdosio
anonymous
  • anonymous
okay thank you guys very much :D
Michele_Laino
  • Michele_Laino
:)

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