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Find the degree of the differential equa...

Find the degree of the differential equation satisfying the relation `sqrt(1+x^2)+sqrt(1+y^2)=lambda(xsqrt(1+y^2)-ysqrt(1+x^2))`

Text Solution

Verified by Experts

The correct Answer is:
`(dy)/(dx) = (1+y^(2))/(1+x^(2))`
Putting x=tanA and y=tanB in the given relation, we get cosA + cosB=`lambda`(sinA-sinB)
or `tan^(-1)x-tan^(-1)y=2tan^(-1)(1/lambda)`
Differentiating w.r.t. to x, we get
`1/(1+x^(2))-1/(1+y^(2))(dy)/(dx)=0`
or `(dy)/(dx)=(1+y^(2))/(1+x^(2))`
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