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Find the general solution of the differe...

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

Text Solution

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The correct Answer is:
`x = 2y^(2) + Cy`.
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y dx + (x - y^(2))dy = 0

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Knowledge Check

  • The general solution of the differential equation (y dx - x dy)/(y ) = 0 is

    A
    `xy = C`
    B
    `x = Cy^(2)`
    C
    `y = Cx`
    D
    `y = Cx^(2)`

  • The general solution of the differential equation (dy)/(dx) = e^(x + y) is

    A
    `e^(x) _ e^(-y) = C`
    B
    `e^(x) + e^(y) = C`
    C
    `e^(-x) + e^(y) = C`
    D
    `e^(-x) + e^(-y) = C`

  • The general solution of the differential equation e^(x) dy + (y e^(x) + 2x)dx = 0 is

    A
    `x e^(y) + x^(2) = C`
    B
    `x e^(y) + y^(2) = C`
    C
    `y e^(x) + x^(2) = C`
    D
    `y e^(y) + x^(2) = C`

    • Similar Questions

    Explore conceptually related problems

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

    Find the general solution of the differential equation (dy)/(dx) - y = cosx.

    Find the general solution of the differential equation x (dy)/(dx) + 2y = x^(2)(x ne 0) .

    Find the general solution of the differential equation (dy)/(dx) = (x+1)/(2 - y), (y ne 2) .

    Show that the general solution of the differential equation (dy)/(dx) + (y^(2) + y + 1)/(x^(2) + x + 1) = 0 is given by ( x + y + 1) = A(1 - x - y - 2xy) , where A is parameter.

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