Home
Class 12
MATHS
The solution of the differential equatio...

The solution of the differential equation `(dx)/(x)+(dy)/(y)=0` is

A

`(1)/(x)+(1)/(y)=C`

B

`logxlogy=C`

C

`xy=C`

D

`x+y=C`

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`(1)/(x)dx+(1)/(y)dy=0`
On integrating, we get
`logx+logy =logCrArr xy =C`.
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|48 Videos

  • DIFFERENTIAL EQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|5 Videos

  • DERIVATIVE AS A RATE MEASURER

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|26 Videos

  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|17 Videos

Similar Questions

Explore conceptually related problems

The solution of differential equation x(dy)/(dx)=y is :

The solution of the differential equation ((x+2y^3)dy)/(dx)=y is

The solution of the differential equation ((dy)/(dx))^(2)-x((dy)/(dx))+y=0 is

The general solution of the differential equation (y dx-x dy)/y=0 is(A) x y = C (B) x=C y^2 (C) y = C x (D) y=C x^2

The general solution of the differential equation (y dx-x dy)/y=0 is (A) x y" "=" "C (B) x=C y^2 (C) y" "=" "C x (D) y=C x^2

Verify that y^2=4a x is a solution of the differential equation y=x(dy)/(dx)+a(dx)/(dy) .

The solution of the differential equation ( dy ) /( dx) +y/x = cos x is :

The solution of differential equation (dy)/(dx)+(y)/(x)=sin x is

The solution of the differential equation (dy)/(dx)=(4x+y+1)^(2) , is

The solution of the differential equation ydx+ (x +x^2 y) dy =0 is

OBJECTIVE RD SHARMA ENGLISH-DIFFERENTIAL EQUATIONS-Chapter Test
  1. The solution of the differential equation (dx)/(x)+(dy)/(y)=0 is

    Text Solution

    |

  2. (x^(2)+y ^(2)) dy = xydx. If y (x (o)) =e, y (1)=1, then the value of ...

    Text Solution

    |

  3. The differential equation of the family of curves y^(2)=4xa(x+1), is

    Text Solution

    |

  4. y=ae^(mx)+be^(-mx) satisfies which of the following differential equat...

    Text Solution

    |

  5. The solution of the differential equation (dy)/(dx)=e^(y+x)+e^(y-x), i...

    Text Solution

    |

  6. The differential equation of the family of curves y=e^(2x)(a cos x+b s...

    Text Solution

    |

  7. The differential equation obtained on eliminating A and B from y=A c...

    Text Solution

    |

  8. The solution of (dy)/(dx)=((y)/(x))^(1//3), is

    Text Solution

    |

  9. The slope of the tangent at (x , y) to a curve passing through a po...

    Text Solution

    |

  10. Solve Y-X(dy)/(dx)=a(y^(2)+(dy)/(dx))

    Text Solution

    |

  11. The solution of the differential equation (x+2y^(2))(dy)/(dx)=y, is

    Text Solution

    |

  12. The general solution of the differential equation (dy)/(dx)+sin((x+y)/...

    Text Solution

    |

  13. The solution of (dy)/(dx)-y=1, y(0)=1 is given by

    Text Solution

    |

  14. The number of solution of y'=(x+1)/(x-1),y(1)=2, is

    Text Solution

    |

  15. What is the solution of y'=1+x+y^(2)+xy^(2),y(0)=0?

    Text Solution

    |

  16. Solution of the differential equation x(dy)/(dx)=y+sqrt(x^(2)+y^(2)), ...

    Text Solution

    |

  17. Integral curve satisfying Y'=(x^2 +y^2)/(x^2-y^2) y' (1) ne 1 has th...

    Text Solution

    |

  18. The differential equation which represents the family of plane curves ...

    Text Solution

    |

  19. A continuously differentiable function y=f(x) , x in ((-pi)/(2) ,(pi)/...

    Text Solution

    |

  20. The solution of the differential equation (d^(2)y)/(dx^(2))=e^(-2x), i...

    Text Solution

    |

  21. The order and degree of the differential equation (d^(2)y)/(dx^(2))=sq...

    Text Solution

    |