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

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

Mathematics
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do u know what to use for them? integrating factors.... etc.. what's the topic?
i dont wanna look for the method...
okay i gotta use integrating factors

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

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