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# differntial equation watch

1. The question i was answering:
Given that k is an arbitrary constant, show that y^2 +kx^2=9k is the general solution of the differential equation dy/dx= -xy/(9-x^2)

So my working:
intergral(1/y)dy = (-)intergral -1/6+2x +1/6-2x (i used partial fractions)

and i worked it through to get y^2 + 4dx^2 = 36d where d is a constant and i don't know if this is right or wrong.

appreciate any guidance, Thanks
2. (Original post by 111davey1)
Given that k is an arbitrary constant, show that y^2 +kx^2=9k is the general solution of the differential equation dy/dx= -xy/(9-x^2)

So my working:
intergral(1/y)dy = (-)intergral -1/6+2x +1/6-2x (i used partial fractions)

and i worked it through to get y^2 + 4dx^2 = 36d where d is a constant and i don't know if this is right or wrong.

appreciate any guidance, Thanks
I think somethings gone wrong in your integration / simplifying. Can you please post your working after the integration of both sides?

EDIT: As the bear points out below, you don't need partial fractions here.
3. in the fraction

-x
-----
1 - x2

you can see that the top is almost the derivative of the underneath, which makes finding the integral very straightforward.
4. (Original post by 111davey1)
Given that k is an arbitrary constant, show that y^2 +kx^2=9k is the general solution of the differential equation dy/dx= -xy/(9-x^2)

So my working:
intergral(1/y)dy = (-)intergral -1/6+2x +1/6-2x (i used partial fractions)

and i worked it through to get y^2 + 4dx^2 = 36d where d is a constant and i don't know if this is right or wrong.

appreciate any guidance, Thanks
See what happens if you substitute k=4d, your answer is of the right form

EDIT: i.e. you've actually solved it.
5. (Original post by notnek)
I think somethings gone wrong in your integration / simplifying. Can you please post your working after the integration of both sides?
ln(y) = -(-1/2ln(6+2x)-1/2ln(6-2x)) + ln(k)

y^2 =(6+2x)(6-2x)k

y^2 = (36-4x^2)k
y^2 = 36k -4kx^2

Thanks
6. (Original post by 111davey1)
Given that k is an arbitrary constant, show that y^2 +kx^2=9k is the general solution of the differential equation dy/dx= -xy/(9-x^2)

So my working:
intergral(1/y)dy = (-)intergral -1/6+2x +1/6-2x (i used partial fractions)

and i worked it through to get y^2 + 4dx^2 = 36d where d is a constant and i don't know if this is right or wrong.

appreciate any guidance, Thanks
Sorry I didn't notice the in your . Your answer is correct but since it's an arbitrary constant you can just use so you get the form required.
7. (Original post by the bear)
in the fraction

-x
-----
1 - x2

you can see that the top is almost the derivative of the underneath, which makes finding the integral very straightforward.
Oh yeah didn't see that thanks
8. (Original post by notnek)
Sorry I didn't notice the in your . Your answer is correct but since it's an arbitrary constant you can just use so you get the form required.
Thanks

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