## 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

1. anonymous
2. anonymous

i'm thinking hyperbolas but not sure

3. anonymous

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

4. 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.

5. anonymous

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

6. anonymous

Does this involve the slope field?

7. anonymous

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

8. anonymous

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

9. Michele_Laino

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

10. anonymous

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

11. anonymous

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

12. anonymous

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

13. Michele_Laino

since C is an arbitrary real constant, whose values can vary inside the set of real numbers, in other words, we have: $\Large C \in \mathbb{R}$

14. Michele_Laino

|dw:1439275918663:dw|

15. 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?

16. anonymous

oh okay so basically its what the graph would look like despite what c could be, right?

17. Michele_Laino

yes! right! they differ only for the value of C

18. anonymous

If the function y C* I mean.

19. anonymous

okay and this graph would look like a parabola despite what c is right?

20. anonymous

Since the graph shows the curves not symmetrical, therefore it cannot be a parabola.

21. anonymous

I mean it cannot be a hyperbola.

22. Michele_Laino

right! @Jdosio

23. anonymous

okay thank you guys very much :D

24. Michele_Laino

:)