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y log y dx - x dy = 0...

`y log y dx - x dy = 0`

Text Solution

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The correct Answer is:
`y = e^(cx)`
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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)`

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    For each of the exercises given below, verify that the given function (implicit or explicit) is a solution of the corresponding differential equation. (i) xy = ae^(x) + be^(-x) + x^(2) : x (d^(2)y)/(dx^(2)) + 2(dy)/(dx) - xy + x^(2) - 2 = 0 (ii) y = e^(x)(a cos x + b sin x) : (d^(2)y)/(dx^(2))- 2(dy)/(dx) + 2y = 0 (iii) y = x sin 3x : (d^(2)y)/(dx^(2)) + 9y - 6 cos 3x = 0 (iv) x^(2) = 2y^(2) log y : (x^(2) + y^(2)(dy)/(dx) - xy = 0

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