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

The solution of the differential equation `(xcoty + log cosx)dy +(logsiny-ytanx) dx=0` is

A

`(sinx)^(y)(cosy)^(x)=c`

B

`(siny)^(x)(cosx)^(y)=c`

C

`(sinx)^(x)(cosy)^(y)=c`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`(xcoty+logcosx)dy+(log siny-ytanx)dx=0`
or `intd(xlogsiny)+intd(ylogcosx)=0`
or `xlogsiny+ylogcosx=logc`
or `(siny)^(x)(cosx)^(y)=c`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Exercise (Multiple)|17 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Exercise (Comprehension)|21 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Exercise 10.9|5 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Numerical Value Type|3 Videos

Similar Questions

Explore conceptually related problems

The solution of the differential equation (x cot y+log cos x)dy+(log sin y-y tan x)dx=0 is

The solution of the differential equation (dy)/(dx)= x log x is

The solution of the differential equation dy/dx +y =cosx is -

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

The solution of the differential equation (x+y)(dx-dy)=dx+dy , is

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

Solution of the differential equation (dy)/(dx)+ycosx=0 is

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

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

CENGAGE-DIFFERENTIAL EQUATIONS-Exercise (Single)
  1. The solution of the differential equation {1+xsqrt((x^2+y^2))}dx+{sqrt...

    Text Solution

    |

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

    Text Solution

    |

  3. The solution of the differential equation (xcoty + log cosx)dy +(logsi...

    Text Solution

    |

  4. If =(e^y-x)^(-1), where y(0)=0 , then y is expressed explicitly as ...

    Text Solution

    |

  5. The general solution of the differential equation, y^(prime)+yvarph...

    Text Solution

    |

  6. The integrating factor of the differential equation (dy)/(dx)(x(log...

    Text Solution

    |

  7. The solution of the differential equation x(x^(2)+1)(dy//dx)=y(1-x^(2)...

    Text Solution

    |

  8. Integrating factor of differential equation cosx(dy)/(dx)+ysinx=1 is (...

    Text Solution

    |

  9. Solution of the equation cos^2x(dy)/(dx)-(tan2x)y=cos^4x ,|x|<pi/4, wh...

    Text Solution

    |

  10. If integrating factor of x(1-x^2)dy+(2x^2y-y-a x^3)dx=0 is e^(intp dx...

    Text Solution

    |

  11. A function y=f(x) satisfies (x+1)f^(prime)(x)-2(x^2+x)f(x)=(e^x^2)/((x...

    Text Solution

    |

  12. The general solution of the equation (dy)/(dx)=1+x y is (a) ( b ) (...

    Text Solution

    |

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

    Text Solution

    |

  14. The solution of the differential equation x^2(dy)/(dx)cos1/x-ysin1/x=-...

    Text Solution

    |

  15. The solution of (dy)/(dx)=(x^2+y^2+1)/(2x y) satisfying y(1)=1 is give...

    Text Solution

    |

  16. The solution of the differential equation (dy)/(dx) = 1/(xy[x^(2)sin...

    Text Solution

    |

  17. The equation of a curve passing through (2,7/2) and having gradient...

    Text Solution

    |

  18. Which of the following is not the differential equation of family of c...

    Text Solution

    |

  19. Tangent to a curve intercepts the y-axis at a point Pdot A line ...

    Text Solution

    |

  20. Orthogonal trajectories of family of the curve x^(2/3)+y^2/3=a^((2/3))...

    Text Solution

    |