Math help

[Svt-Sonic]

Well this seems like the "in" thing to do so I need help on this question in regards to my assignment:

Find the integrating factor, the general solution, and particular soluction satisfying the given initial condition:

xy'+y=2x --------------- y(1)=1

I divide the x so I get:

y'+y/x =2

I think the integrating factor (I(x)) is =x

Integrating factor is found with: e^(integral f(x) dx)

f(x) in this case is 1/x , so I think you get the integrating factor with e^(lnx) Therefore meaning the e and ln cancel correct?


Thanks guys! If you need something cleared up ill be checking back alot.

:beer:

 

[canibus]

:dw:how do you get a number out of letters:shrug:

looks tough, good luck with it

 

[Vigilante]

this is the same class im taking e and ln do cancel each other out but im a little iffy on the rest. also y' is that the derivative or typo or what?

 

[jmk97GT]

well, you are correct with the integrating factor being = x.

I did the rest and got y = x + c and the general solution and y = x as particular when you use the initial condition. Let me double check that because it seems too simple to be correct.

EDIT: heres what I did:

dy/dx + P*y = Q ----> P = 1/x , Q = 2

ok so you have M=x (i use mew for integrating factor)

y*M=integral(Q * M)
y*x=integral(2*x)
y*x=x^2+c
y = x + c -----> y(1) = 1
1 = 1 + c -----> c=0
y = x

 

[jshen]

Given the problem

x=1
y=1

As far back as my memory will let me go..

 

[Svt-Sonic]

well, you are correct with the integrating factor being = x.

I did the rest and got y = x + c and the general solution and y = x as particular when you use the initial condition. Let me double check that because it seems too simple to be correct.

EDIT: heres what I did:

dy/dx + P*y = Q ----> P = 1/x , Q = 2

ok so you have M=x (i use mew for integrating factor)

y*M=integral(Q * M)
y*x=integral(2*x)
y*x=x^2+c
y = x + c -----> y(1) = 1
1 = 1 + c -----> c=0
y = x

Ok, well yes x should =1, the same as y, so I think you are definately right here.
Edit:

OOOOOOOHHHHHHHHH, I was making a very bush league error and I forgot to integrate the y' (yes the ' mean y prime or dy/dx).

Sweet, greatly appreciated!!! Ill try and have a fellow student run over it one time, but I think its definately right.

I owe you a beer!
:beer:

 

[jmk97GT]

No sweat, helps that I'm in the same class this semester. Did first order diff's about a month and a half ago :banana:

 

[Unoid]

I was a math major in college and I think I forgot most of it haha.

I was 4 courses shy of my BS Theory/proof of geometry and algebra were just too boring.
calc 3 and differential wasn't too bad

 

[JDStud6]

whats with all the math homework today?

JD

 

[jmk97GT]

I was a math major in college and I think I forgot most of it haha.

I was 4 courses shy of my BS Theory/proof of geometry and algebra were just too boring.
calc 3 and differential wasn't too bad

Diff is my last math course, minus statistics next semester. Civil engineering :banana:

 

[akula51]

6.02 x 10^23.

+/- 4.

QED

Ack

 

[CPViolation]

:dw:how do you get a number out of letters:shrug:

looks tough, good luck with it

It's called Algebra..
I always hated math.
So what did I do? Get a degree in electronics.
Serves me right..
Jeff