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 one year ago
Whats the integrating factor for the following FODE  I've worked it out but im not sure if its right.
(x+1)f'  xy = x
 one year ago
Whats the integrating factor for the following FODE  I've worked it out but im not sure if its right. (x+1)f'  xy = x

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cwrw238
 one year ago
Best ResponseYou've already chosen the best response.0that should be (x+1) y'  xy = x

cwrw238
 one year ago
Best ResponseYou've already chosen the best response.0first divide through by (x+1) right?

Spacelimbus
 one year ago
Best ResponseYou've already chosen the best response.1So far I end up at \[ \large \mu(x) = (x+1)e^{x} \] In case you got the same, otherwise I would have to take a look again

Spacelimbus
 one year ago
Best ResponseYou've already chosen the best response.1alright, in this case we just need to confirm now if it works out, for the LHS it should be possible to be written in the form of a product rule.

cwrw238
 one year ago
Best ResponseYou've already chosen the best response.0right so its (1+x)e^(x) y'  x e^(x) y = x e^(x) ok?

cwrw238
 one year ago
Best ResponseYou've already chosen the best response.0i must admit i'm struggling a bit with these

Spacelimbus
 one year ago
Best ResponseYou've already chosen the best response.1Exactly, and you can verify for yourself that this is equal as writing \[ \Large \frac{d(y(x+1)e^{x})}{dx}=xe^{x} \] It's a bit edgy to multiply it out, but it worked for me.

cwrw238
 one year ago
Best ResponseYou've already chosen the best response.0right and integrating xe^(x) I got e^(x)(1 + x) + A

Spacelimbus
 one year ago
Best ResponseYou've already chosen the best response.1same here, so far you have. \[\large y(x)(x+1)e^{x}=e^{x}(x+1)+C \]

cwrw238
 one year ago
Best ResponseYou've already chosen the best response.0right so i next divided rhough by e ^(x) to get y(x+1) = 1((1+x) + Ce^x y(x + 1) = Ce^x x  1 and thats my result but the book gives y(x+1) = Ce^x x + 1

Spacelimbus
 one year ago
Best ResponseYou've already chosen the best response.1hmm I wonder why they divide like that, usually you want to solve a differential equation for the explicit form, therefore solving for y(x), this gives me: \[\Large y(x)=\frac{C}{(x+1)e^{x}}1= \frac{Ce^{x}}{x+1}1 \]

cwrw238
 one year ago
Best ResponseYou've already chosen the best response.0yea i dont know why they did that

Spacelimbus
 one year ago
Best ResponseYou've already chosen the best response.1makes no sense to me, I just asked WolframAlpha and our answer seems to be correct.

Spacelimbus
 one year ago
Best ResponseYou've already chosen the best response.1what you did seems correct, just seems like a small failure of plus and minus, in the book apparently.

cwrw238
 one year ago
Best ResponseYou've already chosen the best response.0a typo thanks for your help

cwrw238
 one year ago
Best ResponseYou've already chosen the best response.0oh one thing  when you are working out the Integrating factor you dont add a constant of integration right?

Spacelimbus
 one year ago
Best ResponseYou've already chosen the best response.1yes exactly, you can ignore this one during the process (:
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