## anonymous 5 years ago given y>0 and dy/dx=3x^2+4x/y. if the point (1,sqrt{10}) is on the graph relating x and y, then what is y when x=0?

1. myininaya

do you know to find y given y'?

2. anonymous

dy/dx

3. anonymous

?

4. myininaya

you have to integrate y' to get y

5. myininaya

oh wait

6. myininaya

i didn't see that other y

7. myininaya

is it $y'=\frac{3x^2+4x}{y} ?$

8. anonymous

yes

9. myininaya

ok do you know separation of variables?

10. anonymous

quotient rule product rule ?

11. myininaya

$\frac{dy}{dx}=\frac{3x^2+4x}{y}$ you want y so we need to integrate but before we do that we need to separate our y's from our x's

12. myininaya

$y dy=(3x^2+4x) dx$

13. anonymous

oh yes i know how to do that

14. myininaya

i multiplied y on both sides and I multiplied dx on both sides now we need to integrate both sides

15. myininaya

$\int\limits_{}^{}y dy=\int\limits_{}^{}(3x^2+4x) dx$

16. anonymous

whats that long thing u just put

17. myininaya

$\frac{y^2}{2}=\frac{3x^3}{3}+\frac{4x^2}{2}+C$ whenever you integrate you need to do +C

18. anonymous

i havent learned that thing yet

19. myininaya

its the only way

20. myininaya

21. myininaya

do you know what that means?

22. anonymous

i learned that friday

23. anonymous

yes

24. myininaya

thats with weird symbol means

25. myininaya

what*

26. anonymous

but i dont think i can use that symbol yet

27. myininaya

hmmm... that's weird to me

28. anonymous

oh :/

29. anonymous

its fine i guess i should skip that problem and just ask the teacher 2morrow. ill put up a new one.

30. myininaya

ok but that is all i did was found the antiderivative of both sides with respect to whatever varaible was in d( )

31. anonymous

oh okay thanks either way :)

32. myininaya

np