The order of the differential equation satisfying `sqrt(1-x^4)+sqrt(1-y^4)=a(x^2-y^2)` is

Options

A. 1
B. 2
C. 3
D. none of these

Answer

A

Explanation

We have,
`a(x-y)=sqrt(1-y^(2))+sqrt(1-x^(2))`
Putting `x = sin A, y = sin B,` we get
`cosA+cosB=a(sinA-sinB)`
`rArr" "cot(A-B)/(2)=a`
`rArr" "A-B=2cot^(-1)a`
`rArr" "sin^(-1)x-sin^(-1)y=2 cot^(-1)a`.
Differentiating w.r. to x, we get
`(1)/(sqrt(1-x^(2)))-(1)/(sqrt(1-y^(2)))(dy)/(dx)=0rArr(dy)/(dx)=sqrt((1-y^(2))/(1-x^(2)))`
Clearly, it is differential equation of first order and first degree.