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anonymous

  • 5 years ago

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

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  1. bahrom7893
    • 5 years ago
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    do u know what to use for them? integrating factors.... etc.. what's the topic?

  2. bahrom7893
    • 5 years ago
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    i dont wanna look for the method...

  3. bahrom7893
    • 5 years ago
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    okay i gotta use integrating factors

  4. bahrom7893
    • 5 years ago
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    dy/dt = -5y + Sin(3t)

  5. anonymous
    • 5 years ago
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    by method of undetermined coefficients if possible

  6. bahrom7893
    • 5 years ago
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    dy = -5y dt + Sin3t dt -5y dt + Sin3t dt - dy = 0 (-5y + Sin3t)dt = dy

  7. bahrom7893
    • 5 years ago
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    (-5y + Sin3t)dt - dy = 0 (5y - Sin3t)dt + dy = 0 Now let M = (5y - Sin3t) and N = 1

  8. bahrom7893
    • 5 years ago
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    My (derivative of M w/h respect to y) is = 5 Nx = 0

  9. bahrom7893
    • 5 years ago
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    (My - Nt)/N = (5-0)/1 = 5 (By the way Nx must be Nt too above)

  10. bahrom7893
    • 5 years ago
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    So let's multiply everything in this d.e. by an integrating factor: myu = e^(Integral of 5dx) = e^(5x)

  11. bahrom7893
    • 5 years ago
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    (5e^(5x)y - e^(5x)Sin3t)dt + e^(5x)dy = 0

  12. bahrom7893
    • 5 years ago
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    Now My = Nt = 5e^(5x)

  13. bahrom7893
    • 5 years ago
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    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
    • 5 years ago
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    ok

  15. bahrom7893
    • 5 years ago
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    So now Fx ( x ; y ) = M = (5e^(5x)y - e^(5x)Sin3)dx (x is same as t)

  16. bahrom7893
    • 5 years ago
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    sorry forgot Sin(3x)

  17. bahrom7893
    • 5 years ago
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    F = Integral of M with respect to x.

  18. bahrom7893
    • 5 years ago
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    \[F = \int\limits_{}^{}5*e^{5x}y - e^{5x}Sin(3x) dx\]

  19. bahrom7893
    • 5 years ago
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    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
    • 5 years ago
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    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
    • 5 years ago
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    hey u still here? when is this due... i can email it 2 u 2morrow...

  22. bahrom7893
    • 5 years ago
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    HELLO?

  23. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    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
    • 5 years ago
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    okay? gimme ur email...

  26. bahrom7893
    • 5 years ago
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    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
    • 5 years ago
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    treeclimberbpw@gmail.com thanks btw.

  28. bahrom7893
    • 5 years ago
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    check ur email

  29. bahrom7893
    • 5 years ago
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    this equation is just like one of those; get it in format Mdx + Ndy = 0

  30. bahrom7893
    • 5 years ago
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    and solve like i did...

  31. bahrom7893
    • 5 years ago
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    okay lemme just grab a coffee and shove my head into cold water to wake up lol

  32. bahrom7893
    • 5 years ago
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    okay workin on it

  33. bahrom7893
    • 5 years ago
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    hey emailed you the solution, please click on become a fan if I helped, thanks!

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