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Math Help - Separation of Variables

  1. #1
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    Separation of Variables

    Please on this.

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  2. #2
    MHF Contributor

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    Like the title suggests: separate the variables.
    1. dr= b(cos \theta dr+ r sin \theta d\theta)= b cos \theta dr+ br sin \theta d\theta
    (1- bcos \theta)dr= br sin \theta d\theta
    \frac{dr}{r}= \frac{b sin \theta}{1- bcos \theta} d\theta
    Integrate.

    2. tan^2 y dy+ sin^3 x dx
    This isn't an equation! Is it supposed to be equal to 0? If so tan^2 y dy+ sin^3 x dx= 0 is the same as tan^2 y dy= -sin^3 x dx.
    Integrate.

    3. dx= t(1+ t^2) sec^2 x dt
    \frac{dx}{sec^2 x}= cos^2 x dx= t(1+ t^2)dt
    Integrate.

    4. x dx- \sqrt{a^2- x^2}dy= 0
    x dx= \sqrt{a^2- x^2}dy
    \frac{x}{a^2- x^2}dx= dy
    Integrate.

    5. x dx+ \sqrt{a^2- x^2}dy= 0
    Basically the same as 4.

    6. a^2 dx= x \sqrt{a^2 - x^2} dy
    \frac{a^2 dx}{x\sqrt{a^2- x^2}} = dy
    Integrate.
    Last edited by mr fantastic; June 29th 2009 at 02:46 PM. Reason: Fixed latex (added a })
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  3. #3
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    Thanks.

    many thanks. i will try to solve it.
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