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The solution of differential equation (d...

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

A

`y=tan^(-1)x`

B

`y-x=k(1+xy)`

C

`x=tan^(-1)y`

D

`tan(xy)=k`

Text Solution

Verified by Experts

Given that, `" "(dy)/(dx)=(1+y^(2))/(1+x^(2))`
`rArr" "(dy)/(1+y^(2))=(dx)/(1+x^(2))`
On integrating both sides, we get
`" "tan^(-1)y=tan^(-1)x+C`
`rArr" "tan^(-1)y-tan^(-1)x=C`
`rArr" "tan^(-1)((y-x)/(1+xy))=C`
`rArr" "(y-x)/(1+xy)=tanC`
`rArr" "y-x=tanc(1+xy)`
`rArr" "y-x=K(1+xy)`
where, `" "k=tanC`
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