anonymous
  • anonymous
how would one solve the equation (dy/dt = -5y +sin(3t)) ?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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bahrom7893
  • bahrom7893
do u know what to use for them? integrating factors.... etc.. what's the topic?
bahrom7893
  • bahrom7893
i dont wanna look for the method...
bahrom7893
  • bahrom7893
okay i gotta use integrating factors

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More answers

bahrom7893
  • bahrom7893
dy/dt = -5y + Sin(3t)
anonymous
  • anonymous
by method of undetermined coefficients if possible
bahrom7893
  • bahrom7893
dy = -5y dt + Sin3t dt -5y dt + Sin3t dt - dy = 0 (-5y + Sin3t)dt = dy
bahrom7893
  • bahrom7893
(-5y + Sin3t)dt - dy = 0 (5y - Sin3t)dt + dy = 0 Now let M = (5y - Sin3t) and N = 1
bahrom7893
  • bahrom7893
My (derivative of M w/h respect to y) is = 5 Nx = 0
bahrom7893
  • bahrom7893
(My - Nt)/N = (5-0)/1 = 5 (By the way Nx must be Nt too above)
bahrom7893
  • bahrom7893
So let's multiply everything in this d.e. by an integrating factor: myu = e^(Integral of 5dx) = e^(5x)
bahrom7893
  • bahrom7893
(5e^(5x)y - e^(5x)Sin3t)dt + e^(5x)dy = 0
bahrom7893
  • bahrom7893
Now My = Nt = 5e^(5x)
bahrom7893
  • 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?
anonymous
  • anonymous
ok
bahrom7893
  • bahrom7893
So now Fx ( x ; y ) = M = (5e^(5x)y - e^(5x)Sin3)dx (x is same as t)
bahrom7893
  • bahrom7893
sorry forgot Sin(3x)
bahrom7893
  • bahrom7893
F = Integral of M with respect to x.
bahrom7893
  • bahrom7893
\[F = \int\limits_{}^{}5*e^{5x}y - e^{5x}Sin(3x) dx\]
bahrom7893
  • 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)
bahrom7893
  • 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)
bahrom7893
  • bahrom7893
hey u still here? when is this due... i can email it 2 u 2morrow...
bahrom7893
  • bahrom7893
HELLO?
anonymous
  • 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
bahrom7893
  • 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
bahrom7893
  • bahrom7893
okay? gimme ur email...
bahrom7893
  • 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..
anonymous
  • anonymous
bahrom7893
  • bahrom7893
check ur email
bahrom7893
  • bahrom7893
this equation is just like one of those; get it in format Mdx + Ndy = 0
bahrom7893
  • bahrom7893
and solve like i did...
bahrom7893
  • bahrom7893
okay lemme just grab a coffee and shove my head into cold water to wake up lol
bahrom7893
  • bahrom7893
okay workin on it
bahrom7893
  • bahrom7893
hey emailed you the solution, please click on become a fan if I helped, thanks!

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