Question

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

Answer 1

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

Answer 2

i dont wanna look for the method...

Answer 3

okay i gotta use integrating factors

Answer 4

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

Answer 5

by method of undetermined coefficients if possible

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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?

Answer 14

ok

Answer 15

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

Answer 16

sorry forgot Sin(3x)

Answer 17

F = Integral of M with respect to x.

Answer 18

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

Answer 19

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)

Answer 20

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)

Answer 21

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

Answer 22

HELLO?

Answer 23

hey sorry, a friend stopped by my room asking for help on a euler's method thing.

i have a test over it tomorrow

Answer 24

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

Answer 25

okay? gimme ur email...

Answer 26

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..

Answer 27

treeclimberbpw@gmail.com

thanks btw.

Answer 28

check ur email

Answer 29

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

Answer 30

and solve like i did...

Answer 31

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

Answer 32

okay workin on it

Answer 33

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