Home
Class 12
MATHS
The solution of the DE (dy )/(dx) + ...

The solution of the DE ` (dy )/(dx) + sqrt ((1 -y ^(2))/( 1- x ^(2))) = 0 ` is

A

`"sin"^(-1)x."sin"^(-1)y=C`

B

`"sin"^(-1)x=C"sin"^(-1)y`

C

`"sin"^(-1)x-"sin"^(-1)y=C`

D

`"sin"^(-1)x+"sin"^(-1)y=C`

Text Solution

Verified by Experts

The correct Answer is:
D
We have `(dy)/(dx) +sqrt(1-y^(2))/(sqrt(1-x^(2))) = 0`
`(dy)/(dx) =-sqrt(1-y^(2))/(1-x^(2))`
`int (dy)/(sqrt(1-y^(2)))=-int (dx)/(sqrt(1-x^(2)))`
`"sin"^(-1) "("xsqrt(1-y^(2))+ysqrt(1-x^(2))")"=C`
`xsqrt(1-y^(2))+ysqrt(1-x^(2))=C`
Promotional Banner

Topper's Solved these Questions

  • MOCK TEST 3

    CAREER POINT|Exercise MATHS|30 Videos

  • MOCK TEST 5

    CAREER POINT|Exercise Part (C) (MATHS)|30 Videos

Similar Questions

Explore conceptually related problems

The solution of the DE x (dy)/(dx) = cot y is

The solution of the DE x dy + y dx = 0 is

The general solution of the DE (dy)/(dx) = (sqrt (1 - x ^(2))) (sqrt (1 - y ^(2))) is

The solution of the DE (dy)/(dx) = 1 - x + y - xy is

The solution of the DE (dy)/(dx) = (( 1+y ^(2)))/((1 + x ^(2))) is

The solution of the DE (dy)/(dx) = 2 ^( x + y ) is

The solution of the DE (dy)/(dx) = e ^( x+ y ) is

The solution of the DE (dy)/(dx) = (- 2 xy )/( ( x ^(2) + 1)) is

If a an arbitrary constant, then solution of the differential equation (dy)/(dx)+sqrt((1-y^(2))/(1-x^(2)))=0 is

The solution of (dy)/(dx) + sqrt(((1-y^(2))/(1-x^(2))))=0 is

CAREER POINT-MOCK TEST 4-MATHS
  1. If coses 0=(x^(2)-Y^(2))/(x^(2)+Y^(2)) is true iff-

    Text Solution

    |

  2. The area bounded by the curves y= "sin" x, y= cos x and y-axis in 1 qu...

    Text Solution

    |

  3. The solution of the DE (dy )/(dx) + sqrt ((1 -y ^(2))/( 1- x ^(2))...

    Text Solution

    |

  4. A variable circle having fixed radius 'a' passes through origin and me...

    Text Solution

    |

  5. The chord A B of the parabola y^2=4a x cuts the axis of the parabola a...

    Text Solution

    |

  6. If tangents are drawn to the ellipse x^2+2y^2=2, then the locus of the...

    Text Solution

    |

  7. f(x) = ("tan" x^(5))e^(x^(3)"sgn"x^(7)) " is " -

    Text Solution

    |

  8. "if y"="cos"^(-1)((5"cos" x-12 "sin"x)/(13)), where x in (0,(pi)/(2)...

    Text Solution

    |

  9. lim(x to0) ((1+a^(3))+8e^(1//x))/(1+(1-b^(3))e^(1//x))=2 " then "-

    Text Solution

    |

  10. If veca,vecb,vecc are three mutually perpendicular vectors, then the v...

    Text Solution

    |

  11. A straight line moves so that the sum of the reciprocals of its interc...

    Text Solution

    |

  12. The points (1,1), (0, "sec"^(2) 0), ("cosec"^(2) 0,0 ) are collinear f...

    Text Solution

    |

  13. The equation of a line which passes through point A(1,0,-1) and perper...

    Text Solution

    |

  14. The curve y=ax^(3)+bx^(2)+cx is inclined by 45^(@) to x-axis at origi...

    Text Solution

    |

  15. If x^(2) +ax - 3x-(a+2) = 0 has real and distinct roots, then minimum ...

    Text Solution

    |

  16. i=int(e^(x))/((x+2)){1+(x+2)log(x+2)}dx=

    Text Solution

    |

  17. If R is a relation on N as R= {(1+ x, 1+x^2): x <= 5, X in N} which of...

    Text Solution

    |

  18. Cosnsider the system of equation a(1)x+b(1)y+c(1)z=0, a(2)x+b(2)y+c(...

    Text Solution

    |

  19. A sample of 35 observations has the means 80 and SD. As 4. A second sa...

    Text Solution

    |

  20. If A and B are two square matrices such that B=-A^(-1)BA, then (A+B)...

    Text Solution

    |