First order differential equations question

Mutleybm1996

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I don't see in this case why integral d/dx (x/(x+1)) = integral 1/(x+1) ? Could someone possibly explain? I know how this method works, just not why it's playing up here, i can't get it to work. I'm tempted to just say it is as the final equation is the answer in the book :/

Posted from TSR Mobile

(edited 9 years ago)

Reply 1

Mutleybm1996

OP

19

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Once again, I'm not sure why this is the case

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Reply 2

brianeverit

9

Original post by Mutleybm1996

I don't see in this case why integral d/dx (x/(x+1)) = integral 1/(x+1) ? Could someone possibly explain? I know how this method works, just not why it's playing up here, i can't get it to work. I'm tempted to just say it is as the final equation is the answer in the book :/

Posted from TSR Mobile

From your last line, it follows that

\frac{xy}{x+1}=\int \frac{1}{x+1}\text{d}x

(edited 9 years ago)

Reply 3

Hasufel

16

not really sure what`s confusing you - you have it correct:

Your last line is of the form, when you multiply through by the integrating factor and integrate: