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The solution of the differential equatio...

The solution of the differential equation `x^2(dy)/(dx)-xy=1+cos""(y)/x` is

A

`tan""y/(2x)=c-1/(2x^2)`

B

`tan""y/x=c+1/x`

C

`cos""y/x=1+c/x`

D

`x^2=(c+x^2).tan""y/x`.

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The correct Answer is:
A
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Knowledge Check

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

    A
    `x+y=x^2/2+c`
    B
    `x-y=1/3x^3+c`
    C
    `xy=1/4x^4+c`
    D
    `y-x=1/4x^4+c`

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

    A
    `1/(x+y)=c`
    B
    `sin^(-1)(x+y)=x+c`
    C
    `tan^(-1)(x+y)=c`
    D
    `tan^(-1)(x+y)=x+c`

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

    A
    `(1)/(x+y)=c`
    B
    `sin^(-1)(x+y)=x+c`
    C
    `tan^(-1)(x+y)=c`
    D
    `tan^(-1)(x+y)=x+c`

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