## anonymous 5 years ago what is the exact values of y(2) if given dy/dx sin(xy)

1. myininaya

that is dy/dx=sin(xy) ?

2. anonymous

yes

3. myininaya

integrate both sides with respect to x

4. myininaya

5. anonymous

i think u are right but im have trouble integrating it

6. myininaya

i was gonna say treat y like a constant

7. anonymous

i did but i didnt get the right answer

8. anonymous

the final answer is y(2) 1.632.

9. myininaya

here is what i was going to do so we intergate dy/dx with respect to x and get y we integrate the other side with respect to x and get 1/y*(-cos(xy))

10. myininaya

+C

11. anonymous

how did you get 1/y

12. myininaya

find $\int\limits_{}^{}\sin(3x)dx$

13. anonymous

it would be -1/3cos3x

14. myininaya

right so if we are treating y like a constant then what is $\int\limits_{}^{}\sin(xy)dx$

15. anonymous

ok so what do i plug in y if given x=2

16. myininaya

but see i don't think this right i think we need to separtation of varaibles? but i don't know how to expand sin(xy) i'm thinking on this part

17. anonymous

this is about using eulers method

18. anonymous

by the way

19. myininaya

ok eulers method let me look into it chag do you have any thoughts?

20. myininaya

so we don't know what y(2) is right?

21. anonymous

right we want to find the actual value

22. myininaya

i'm learning right now about eulers method

23. anonymous

oh ok

24. anonymous

i know i have to find the integral bu i do not know what to plug in for y

25. anonymous

they gave me initial value but i do not think that would elp

26. anonymous

*help

27. myininaya

nath this is harder than what i would thought it would be

28. myininaya

http://www.math.tamu.edu/REU/comp/matode.pdf scroll to page 16 this might help