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differntial equation Watch

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    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
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    (Original post by 111davey1)
    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
    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.
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    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.
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    (Original post by 111davey1)
    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
    See what happens if you substitute k=4d, your answer is of the right form

    EDIT: i.e. you've actually solved it.
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    (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
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    (Original post by 111davey1)
    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
    Sorry I didn't notice the d in your 4dx^2. Your answer is correct but since it's an arbitrary constant you can just use k=4d so you get the form required.
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    (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
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    (Original post by notnek)
    Sorry I didn't notice the d in your 4dx^2. Your answer is correct but since it's an arbitrary constant you can just use k=4d so you get the form required.
    Thanks
 
 
 
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