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The solution the differential equation ...

The solution the differential equation
`"cos x sin y dx" + "sin x cos y dy" =0` is

A

`(sin x)/(sin y)=C`

B

`sin x sin y =C`

C

`sin x+sin y =C`

D

`cos x cos y =C`

Text Solution

Verified by Experts

The correct Answer is:
B
Given differential equation is
`cos x sin ydx+ sin x cos ydy=0`
`Rightarrow (cos x)/(sinx )dx=(cos y)/(sin y)dy`
`Rightarrow cot x dx=-cot ydy`
On integrating both sides, we get
`log sin x=-log sin y+log C`
`Rightarrow log sin x siny=logC`
`Rightarrow sinx. siny=C`
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NCERT EXEMPLAR-DIFFERENTIAL EQUATIONS -Differential Equations
  1. The integrating factor of differential equation (dy)/(dx)+y=(1+y)/(x)"...

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  2. y=ae^(mx)+b^(-mx) satisfies which of the following differential equati...

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  3. The solution the differential equation "cos x sin y dx" + "sin x c...

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  4. The solution of x(dy)/(dx)+y=e^(x)"is"

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  5. The differential equation of the family of curves of x^(2)+y^(2)-2ay=0...

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  6. The family y=Ax+A^(3) of curves is represents by differential equation...

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  7. The general solution of (dy)/(dx)=2xe^(x^(2)-y) is

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  8. The curve for which the slope of the tangent at any point is equal to ...

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  9. The general solution of differential equation (dy)/(dx)=e^((x^(2))/(2)...

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  10. The solution of equation (2y-1)dx-(2x+3)dy=0 is

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  11. The differential equation for which y=a cos x+b sin x is a solution is

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  12. The solution of (dy)/(dx)+y=e^(-x), y(0)=0 "is"

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  13. The order and degree of differential equation: ((d^(3)y)/(dx^(3)))^(...

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  14. The order and degree of differential equation: [1+((dy)/(dx))^(2)]=(d^...

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  15. The differential equation of family of curves of y^(2)=4a(x+a)is

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  16. Which of the following is a general solution of (d^(2)y)/(dx^(2))-2(dy...

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  17. The general solution of (dy)/(dx)+y tan x=sec x is

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  18. The solution of differential equation (dy)/(dx)+(y)/(x)=sin x is

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  19. The general solution of differential equation (dy)/(dx)=e^((x^(2))/(2)...

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  20. The solution of differential equation (dy)/(dx)=e^(x-y)+x^(2)e^(-y)is

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