Integrate by substitution

  • #1

Homework Statement


The problem states: Use substitution to solve:

y'=1/(x+y)^2-1


Homework Equations





The Attempt at a Solution



I used the substitution of v=x+y

resulting in the answer y=[3(x-C)]^(1/3) - x

but I'm not too sure that's right

Can some help with the answer and the steps for getting it. It's just for a practice test so I'm not graded on it.
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
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Show all of the steps you took to get the correct answer. If you made an error in any step, we could point it out then.
 
  • #3
gabbagabbahey
Homework Helper
Gold Member
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Homework Statement


The problem states: Use substitution to solve:

y'=1/(x+y)^2-1


Homework Equations





The Attempt at a Solution



I used the substitution of v=x+y

resulting in the answer y=[3(x-C)]^(1/3) - x

but I'm not too sure that's right

Can some help with the answer and the steps for getting it. It's just for a practice test so I'm not graded on it.

It looks like you got to [itex](x+y)^3=3x+C[/itex] correctly (you probably had -3C instead of +C but it makes no difference since both are just undetermined constants) ? ...If so, this is how you should leave your answer (unless you are given a point on the curve y(x)). The reason being is that there are actually three roots to this cubic equation, and [itex]y+x=\sqrt[3]{3x+C}[/itex] is only one of them.
 
  • #4
Great! So overall I got the problem right. Thanks.
 

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