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(a)dy/dx = (xy)/(x^2+y^2)...

(a)`dy/dx = (xy)/(x^2+y^2)`

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dy/dx=(2xy)/(x^2-1-2y)

The solution of the differential equation (dy)/(dx)=(xy)/(x^(2)+y^(2)) is

Knowledge Check

  • If (dy)/dx = (xy)/(x^2 + y^2), y(1) = 1 and y(x) = e then x =

    A
    `(sqrt3/2)e`
    B
    `sqrt3e`
    C
    `sqrt2e`
    D
    `e/sqrt2`

  • If (dy)/(dx) = ( xy)/( x ^(2) + y ^(2)) , y (1) = 1 and y (x _(0)) = e, then x _(0) = _____

    A
    `sqrt ( 3e)`
    B
    `sqrt3e`
    C
    `sqrt (2 ( e ^(2) -1))`
    D
    e

  • The solution of the differential (dy)/(dx) = (xy)/(x^(2) + y^(2)) , is

    A
    `ay^(2) = e^(x^(2))/e^(y^(2))`
    B
    `ay = ex^(x"/" y)`
    C
    `y = e^(x^2) + e^(y^2) + C`
    D
    `y = e^(x^2) + y^(2) + C`

    • Similar Questions

    Explore conceptually related problems

    Find the particular solution of eh differential equation (dy)/(dx)=(xy)/(x^(2)+y^(2)) given that y=1 when x=0.

    (dy)/(dx)=(2xy)/(x^(2)-y^(2))

    (dy)/(dx)=(x^2y+y)/(xy^2+x)

    (dy)/(dx) = (2xy)/(x^(2)-1-2y)

    STATEMENT -1 : The differential equation (dy)/(dx) = (2xy)/(x^(2) + y^(2)) Can't be solved by the substitution x = vy. and STATEMENT-2 : When the differential equation is homogeneous of first order and first degree, then the substitution that solves the equation is y = vx.

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