Integrate by substitution

Homework Statement

The problem states: Use substitution to solve:

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

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

rock.freak667
Homework Helper
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.

gabbagabbahey
Homework Helper
Gold Member

Homework Statement

The problem states: Use substitution to solve:

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

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 $(x+y)^3=3x+C$ 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 $y+x=\sqrt[3]{3x+C}$ is only one of them.

Great! So overall I got the problem right. Thanks.