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The solution of the differential equatio...

The solution of the differential equation
` x dx + y dx = (x dy - y dx)/(x^(2)+y^(2))=0` is

A

`y = x tan ((x^(2) + y^(2) + C)/(2))`

B

`x = y tan ((x^(2) + y^(2) + C)/(2))`

C

`y = x tan ((C - x^(2) - y^(2))/(2))`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
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Knowledge Check

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

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

  • 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(dy)/(dx)+y = y^2 is

    A
    y=1+cxy
    B
    y=log (cxy)
    C
    y+1 = cxy
    D
    y=c+xy

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