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Find the general solution of sqrt(1-x^(...

Find the general solution of `sqrt(1-x^(2))dy +sqrt(1-y^(2))dx=0`.

Text Solution

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The correct Answer is:
`sin^(-1)x+sin^(-1)y=c`
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Find the general solution of x+y(dy)/(dx)=0.

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Knowledge Check

  • The solution of sqrt(1 - x^(2)) dx + sqrt(1 - y^(2)) dy = 0 is

    A
    `x sqrt(1-x^(2)) + y sqrt(1- y^(2)) + "Cosh"^(-1) x + "Cosh"^(-1) y = c`
    B
    `x sqrt(1 + x^(2)) + y sqrt(1 + y^(2)) = c`
    C
    `x sqrt(1 + x^(2)) - y sqrt(1 + y^(2)) + "Sinh"^(-1) x - "Sinh"^(-1) y = c`
    D
    `Sinh^(-1) x + Sinh^(-1) y=c`

  • The solution of sqrt(1+x^(2))dx + sqrt(1+y^(2)) dy = 0 is

    A
    `xsqrt(1+x^(2)) + ysqrt(1+y^(2)) + sin h^(-1)x + sin h^(-1) y = c`
    B
    `xsqrt(1+x^(2)) + ysqrt(1+y^(2)) = c`
    C
    `xsqrt(1+x^(2)) - ysqrt(1+y^(2)) + sin h^(-1)x - sin h^(-1) y = c`
    D
    `sin h^(-1) x + sin h^(-1)y = c`

  • The solution of sqrt(1 + x^(2)) dx + sqrt(1 + y^(2)) dy = 0 is

    A
    `x sqrt(1 + x^(2)) + y sqrt(1 + y^(2)) + Sinh^(-1) x + Sinh^(-1) y = c`
    B
    `x sqrt(1 + x^(2)) + y sqrt(1 + y^(2)) = c`
    C
    `x sqrt(1 + x^(2)) - y sqrt(1 + y^(2)) + Sinh^(-1) x - Sinh^(-1) y = c`
    D
    `Sinh^(-1) x + Sinh^(-1) y = c`

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    Solve sqrt(1+x^(2)) sqrt(1+y^(2))dx+xy dy=0

    The general solution of x sqrt(1 + y^(2)) dx + y sqrt(1 + x^(2)) dy = 0 is

    The solution of x sqrt(1 - y^(2)) dx + y sqrt(1 - x^(2)) dy = 0 is

    The general solution of (dy)/(dx) + (sqrt(1 - y^(2)))/(sqrt(1 - x^(2))) = 0 is

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