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The solution of the differential equatio...

The solution of the differential equation
`(1+x^(2))(dy)/(dx)+1+y^(2)=0`, is

A

`tan^(-1)x-tan^(-1)y=tan^(-1)C`

B

`tan^(-1)y-tan^(-1)x=tan^(-1)C`

C

`tan^(-1)y pm tan^(-1)x=tanC`

D

`tan^(-1)y+tan^(-1)x=tan^(-1)C`

Text Solution

Verified by Experts

The correct Answer is:
D
If `tan^(-1)y+tan^(-1)x=tan^(-1)C`, then
`(d)/(dx)(tan^(-1)y)+(d)/(dx)(tan^(-1)x)=0`
`rArr" "(1)/(1+y^(2))(dy)/(dx)+(1)/(1+x^(2))=0rArr(1+x^(2))(dy)/(dx)+(1)/(1+y^(2))=0`
Hence, `tan^(-1)x+tan^(-1)y=tan^(-1)C` is the solution of the given differential.
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OBJECTIVE RD SHARMA-DIFFERENTIAL EQUATIONS-Chapter Test
  1. The solution of the differential equation (1+x^(2))(dy)/(dx)+1+y^(2)...

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  2. If (x^2+y^2)dy=xydx and y(1)=1 and y(xo)=e, then xo=

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  3. The differential equation of the family of curves y^(2)=4xa(x+1), is

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  4. y=ae^(mx)+be^(-mx) satisfies which of the following differential equat...

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  5. The solution of the differential equation (dy)/(dx)=e^(y+x)+e^(y-x), i...

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  6. The differential equation of the family of curves y=e^(2x)(a cos x+b s...

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  7. The differential equation obtained by eliminating A and B from y = A c...

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  8. The solution of (dy)/(dx)=((y)/(x))^(1//3), is

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  9. The slope of the tangent at (x , y) to a curve passing through a po...

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  10. The solution of the differential equaton y-x(dy)/(dx)=a(y^(2)+(dy)/(...

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

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  12. The general solution of the differential equation (dy)/(dx)+sin(x+y)/2...

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  13. The solution of (dy)/(dx)-y=1, y(0)=1 is given by y(x)=

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  14. The number of solution of y'=(x+1)/(x-1),y(1)=2, is

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  15. What is the solution of y'=1+x+y^(2)+xy^(2),y(0)=0?

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  16. solution of the differential equation xdy-ydx=sqrt(x^2+y^2 )dx is

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  17. Integral curve satisfying y'=(x^2+y^2)/(x^2-y^2), has the slope at th...

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  18. The differential equation which represents the family of plane curves ...

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  19. A continuously differentiable function phi(x)in (0,pi//2) satisfying y...

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  20. The solution of the differential equation (d^(2)y)/(dx^(2))=e^(-2x), i...

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  21. The order and degree of the differential equation (d^(2)y)/(dx^(2))=sq...

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