Home
Class 12
MATHS
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

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.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise MULTIPLE CORRECT ANSWERS TYPE|17 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise Linked Comprehension types|21 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISES 10.9|5 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Archives|14 Videos

Similar Questions

Explore conceptually related problems

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

The degree of the differential equation satisfying by the curves sqrt(1+x)-asqrt(1+y)=1, is ……..

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

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

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))

Find the solution of the differential equation x\ sqrt(1+y^2)dx+y\ sqrt(1+x^2)dy=0.

Solve the following differential equation: x\ sqrt(1-y^2)dx+y\ sqrt(1-x^2)\ dy=0

The general solution of the differential equation sqrt(1-x^(2)y^(2)) dx = y dx + x dy is

Solve the following differential equation: \ y\ sqrt(1+x^2)+x\ sqrt(1+y^(2\ ))(dy)/(dx)\ =0

The order and degree of the differential equation (d^(2)y)/(dx^(2))=sqrt(1+((dy)/(dx))^(3)) , is

Home
Profile