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

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

Spacelimbus
 2 years 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
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0i must admit i'm struggling a bit with these

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

Spacelimbus
 2 years 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
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0yea i dont know why they did that

Spacelimbus
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0a typo thanks for your help

cwrw238
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.1yes exactly, you can ignore this one during the process (:
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