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Solution of differential equation (dy...

Solution of differential equation
`(dy)/(dx)=sin (x+y)+cos(x+y)` is equal to

A

`log (2+ "sec" (x+y)/(2))=x + C`

B

`log (1+ tan (x+y))= x + C`

C

`log (1+ "tan" (x+y)/(2))=y +C`

D

`log (1+ "tan " (x+y)/(2))=x +C`

Text Solution

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The correct Answer is:
D
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Knowledge Check

  • Solution of the differential equation (dy)/(dx)=sin(x+y)+cos(x+y) is

    A
    `log|1+tan((x+y)/2)|=y+c`
    B
    `log|2+sec((x+y)/2)|=x+c`
    C
    `log|1+tan(x+y)|=y+c`
    D
    none of these

  • The solution of differential equation (dy)/(dx)-3y= sin 2x is

    A
    `y=e^(-3x) ((cos 2x+3 sin 2x)/(13))+c`
    B
    `y= e^(-3x) ((cos 2x- 3 sin 2x)/(13)) +c`
    C
    `ye^(-3x) = -w^(-3x) ((2 cos 2x + 3 sin 2x)/(13))+c`
    D
    None of these

  • Solution of the differential equation (y+x(dy)/(dx))sin(xy)=cosx is

    A
    sinx+cos(xy)=c
    B
    sinx-cos(xy)=c
    C
    cosx+sin(xy)=c
    D
    cosx-sin(xy)=c

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