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The degree of the differential equation ...

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

A

1

B

2

C

3

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
1) Putting `x=sinA` and `y=sinB` in the given relation, we get
`cosA+cosB=a(sinA-sinB)`
or `A-B=2cot^(-1)a`
or `sini^(-1)x-sin^(-1)y=2cot^(-1)a`
Differentiating w.r.t. x, we get
`1/sqrt(1-x^(2))-1/sqrt(1-y^(2))(dy)/(dx)=0`
Clearly, it is differential equation of degree one.
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Knowledge Check

  • The degree of the differential equation satisfying sqrt(1-x^2)+sqrt(1-y^2)=b(x-y) is

    A
    1
    B
    3
    C
    4
    D
    0

  • The degree of the differential equation satisfying (sqrt(1+x^2)+ sqrt(1+y^2))= A(x sqrt(1+y^2)-y sqrt(1+x^2)) is

    A
    `2`
    B
    `3`
    C
    `4`
    D
    None

  • The degree of the differential equation satifying sqrt(1+x^2)+sqrt(1+y^2)=A(xsqrt(1+y^2)-ysqrt(1+x^2)) is

    A
    2
    B
    3
    C
    4
    D
    none of these

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