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Let y=g(x) be the solution of the diffe...

Let `y=g(x)` be the solution of the differential equation `sinx ((dy)/(dx))+y cos x=4x, x in (0,pi)` If `y(pi/2)=0`, then `y(pi/6)` is equal to

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Knowledge Check

  • Let y=y(x) be the solution of the differential equation sinxdy/dx+ycosx=4x,x in(0,pi) . If y(pi/2)=0 , then y(pi/6) is equal to

    A
    `-8/(9sqrt(3))pi^2`
    B
    `-8/9pi^2`
    C
    `-4/9pi^2`
    D
    `4/(9sqrt(3))pi^2`

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

    A
    `tan^(-1)"" (x)/(y) + (1)/(2) log (x^(2) + y^(2)) = C`
    B
    ` tan^(-1)"' (y)/(x) - (1)/(2) log(x^(2) + y^(2)) = C`
    C
    `cot^(-1)"" ((y)/(x)) + (1)/(2) log (x^(2) + y^(2) = C`
    D
    None of the above

  • The solution of the differential equation x sin d (dy)/(dx) + ( x cos x + sin x ) y = sinx . When y (0)=0 is

    A
    ` xy sin x = 1- cos x `
    B
    `xy sin x + cos x =0`
    C
    `x sin x + y cos x =0`
    D
    `x sin x + y cos x =1 `

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    The solution of the differential equation y sin (x//y) dx= (x sin (x//y)-y) dy satisfying y(pi//4)=1 is

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