## anonymous 5 years ago how would one solve the equation (dy/dt = -5y +sin(3t)) ?

1. bahrom7893

do u know what to use for them? integrating factors.... etc.. what's the topic?

2. bahrom7893

i dont wanna look for the method...

3. bahrom7893

okay i gotta use integrating factors

4. bahrom7893

dy/dt = -5y + Sin(3t)

5. anonymous

by method of undetermined coefficients if possible

6. bahrom7893

dy = -5y dt + Sin3t dt -5y dt + Sin3t dt - dy = 0 (-5y + Sin3t)dt = dy

7. bahrom7893

(-5y + Sin3t)dt - dy = 0 (5y - Sin3t)dt + dy = 0 Now let M = (5y - Sin3t) and N = 1

8. bahrom7893

My (derivative of M w/h respect to y) is = 5 Nx = 0

9. bahrom7893

(My - Nt)/N = (5-0)/1 = 5 (By the way Nx must be Nt too above)

10. bahrom7893

So let's multiply everything in this d.e. by an integrating factor: myu = e^(Integral of 5dx) = e^(5x)

11. bahrom7893

(5e^(5x)y - e^(5x)Sin3t)dt + e^(5x)dy = 0

12. bahrom7893

Now My = Nt = 5e^(5x)

13. bahrom7893

wow sorry about that, i keep confusing t with x, everywhere x means t, now let me just switch to x, cuz i keep getting mixed up... t is same as x, okay?

14. anonymous

ok

15. bahrom7893

So now Fx ( x ; y ) = M = (5e^(5x)y - e^(5x)Sin3)dx (x is same as t)

16. bahrom7893

sorry forgot Sin(3x)

17. bahrom7893

F = Integral of M with respect to x.

18. bahrom7893

$F = \int\limits_{}^{}5*e^{5x}y - e^{5x}Sin(3x) dx$

19. bahrom7893

Sorry i'll have to leave now, so just to finish this, integrate that with respect to x to get something like: e^(5x)y -.................. +h(y)

20. bahrom7893

then you will have: F = e^(5x)y -.................. +h(y). Differentiate the expression you get with respect to y to get: Fy = e^(5x) - or plus ............... +h'(y) Set Fy = N and solve for h'(y) then integrate h'(y) to find h(y) and plug that into F(x;y)

21. bahrom7893

hey u still here? when is this due... i can email it 2 u 2morrow...

22. bahrom7893

HELLO?

23. anonymous

hey sorry, a friend stopped by my room asking for help on a euler's method thing. i have a test over it tomorrow

24. bahrom7893

hey ima send u a couple of examples that use the same principle that were solved out by me, sorry im too tired right now

25. bahrom7893

okay? gimme ur email...

26. bahrom7893

bpw12 gimme an email, i will send u a couple of solved problems that use the same method.. follow them and solve this the same way, sorry too tired now..

27. anonymous

treeclimberbpw@gmail.com thanks btw.

28. bahrom7893

check ur email

29. bahrom7893

this equation is just like one of those; get it in format Mdx + Ndy = 0

30. bahrom7893

and solve like i did...

31. bahrom7893

okay lemme just grab a coffee and shove my head into cold water to wake up lol

32. bahrom7893

okay workin on it

33. bahrom7893

hey emailed you the solution, please click on become a fan if I helped, thanks!