- #1

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USE SUBSTITUTION u=x^2+y^2

I tried to work it out but got a really ugly answer, please help!

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- Thread starter aatkins09
- Start date

- #1

- 7

- 0

USE SUBSTITUTION u=x^2+y^2

I tried to work it out but got a really ugly answer, please help!

- #2

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- 0

- #3

- 7

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I got

int(y dy)=int(-x+sqrt(u))dx

which turned into

y^2/2=(1/-2+2y)*int(sqrt(u) du)

which equals

-1/2+2y*2/3u^3/2

which then gets down to

y^2/2=(-u^(3/2))/3-3y

and then it gets uglier when I try to get y by itself

I know I am messing up somewhere but cannot pin point it

- #4

uart

Science Advisor

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- #5

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du/dx would be 2x+2y but I dont understand where to go from there. how can I replace dy/dx with it?

- #6

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du/dx would be 2x+2y but I dont understand where to go from there. how can I replace dy/dx with it?

Remember that you have to use implicit differentiation.

[tex]du=2xdx+2ydy[/tex]

Then you can solve for [tex]dy/dx[/tex]

You should find that when you find this and substitute, several things should cancel.

- #7

- 7

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Remember that you have to use implicit differentiation.

[tex]du=2xdx+2ydy[/tex]

Then you can solve for [tex]dy/dx[/tex]

You should find that when you find this and substitute, several things should cancel.

I did it (in my head, not on paper yet) and I'm pretty sure I've got it! thank you so much, I appreciate all of your help!

- #8

- 7

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Remember that you have to use implicit differentiation.

[tex]du=2xdx+2ydy[/tex]

Then you can solve for [tex]dy/dx[/tex]

You should find that when you find this and substitute, several things should cancel.

nvm, I still can't get it. it's okay though, thank you, I appreciate all of your help!

- #9

uart

Science Advisor

- 2,776

- 9

nvm, I still can't get it. it's okay though, thank you, I appreciate all of your help!

[tex] \frac{du}{dx} = 2x+2y \, \frac{dy}{dx}[/tex]

Now just substitute in your original expression for dy/dx and it literally just falls into place.

- #10

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[tex] \frac{du}{dx} = 2x+2y \, \frac{dy}{dx}[/tex]

Now just substitute in your original expression for dy/dx and it literally just falls into place.

Thanks so much :)

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