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

Question

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

anonymous · Answer

http://www.wolframalpha.com/widgets/view.jsp?id=e602dcdecb1843943960b5197efd3f2a

anonymous · Answer

i'm thinking hyperbolas but not sure

anonymous · Answer

$$dy=0.2x dx$$
by moving over

$$\int\limits dy=\int\limits 0.2x dx$$
Is that what you did?

anonymous · Answer

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 · Answer

um .. no i just shamelessly plugged it into wolfram :P

anonymous · Answer

Does this involve the slope field?

anonymous · Answer

it might, some of the other questions iv been asked have involved the slope field

anonymous · Answer

plug the equation into wolfram and scroll down to the family curve , it seems to show a parabola or hyperbola

michele_laino · Answer

after a simple integration I got this:
$$\Large \int {dy = 0.2\int {xdx}  = 0.2 \cdot \frac{{{x^2}}}{2}}  + C$$

anonymous · Answer

Seems like a parabola. Any 2 curves symmetrical is a hyperbola.

anonymous · Answer

oh yea. I took derivative instead of integrating it..

anonymous · Answer

okay can you just explain to me what the hell family curves are ?

michele_laino · Answer

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 · Answer

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