Home
Class 12
MATHS
x(dy)/(dx)=y(logy-logx+1)...

`x(dy)/(dx)=y(logy-logx+1)`

A

`logx/y=cy`

B

`logy/x=cy`

C

`logy/x=cx`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`(dy)/(dx)= y/x[logy/x+1]`
Put `y=vx`
`v+x(dv)/(dx) = vlogv+v`
`therefore (dv)/(vlogv) = (dx)/x`
`therefore log(logv)=logx+logc=logcx`
`therefore logy/x=cx`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Archives|14 Videos

Similar Questions

Explore conceptually related problems

(dy)/(dx)=x+y

If x^(logy)=logx , prove that, (x)/(y).(dy)/(dx)=(1-logx log y)/((log x)^(2))

If y=e^(x^(e ^(x^(...oo)))) ,show that, (dy)/(dx)=(y^(2)logy)/(x(1-y log x logy)) .

If y=a^(x^(a^(x^(…oo)))) , show that, (dy)/(dx)=(y^(2)logy)/(x(1-y log x log y)) .

If x^(y) =e^(x-y) , prve that , (dy)/(dx) =(logx)/((log ex)^(2)) .

(dy)/(dx)=1-x+y-xy

(dy)/(dx)=1+x+y+xy

If y=x+1/(x+1/(x+1/(x+\ dot))) , prove that (dy)/(dx)=y/(2y-x) .

If y=x^(y^(x)) , prove that, (dy)/(dx)=(y log y(1+x logx log y))/(x logx(1-x logy)) .

If x=y^(y^(y^(...oo))) , then show that, (dy)/(dx)=(y(1-x logy))/(x^(2)) .

CENGAGE PUBLICATION-DIFFERENTIAL EQUATIONS-All Questions
  1. The solution of the differential equation y^-8y^=0, where y(0)=1/8,y^(...

    Text Solution

    |

  2. The slope of the tangent at (x , y) to a curve passing through (1,p...

    Text Solution

    |

  3. x(dy)/(dx)=y(logy-logx+1)

    Text Solution

    |

  4. The solution of differential equation x y^(prime)=x((y^2)/(x^2)+(f((y^...

    Text Solution

    |

  5. The solution of (x^2+x y)dy=(x^2+y^2)dx is (a) ( b ) (c)logx=log(( d ...

    Text Solution

    |

  6. The solution of (y+x+5)dy=(y-x+1)dx is (a) ( b ) (c)log(( d ) (e) (f)...

    Text Solution

    |

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

    Text Solution

    |

  8. Solutionof the differential equation ydx-xdy+xsqrt(xy)dy=0 is

    Text Solution

    |

  9. The solution of x^(2)(dy)/(dx)-xy=1+cosy/x is

    Text Solution

    |

  10. The solution of the differential equation 2x ^(2)y (dy)/(dx) = tan ( x...

    Text Solution

    |

  11. The solution of the differential equation {1/x-y^(2)/(x-y)^(2)}dx+{x^...

    Text Solution

    |

  12. The solution of differential equation (2y+x y^3)dx+(x+x^2y^2)dy=0 is (...

    Text Solution

    |

  13. The solution of y e^(-x/y)dx-(x e^((-x/y))+y^3)dy=0 is (a) ( b ) (c...

    Text Solution

    |

  14. The curve satisfying the equation (dy)/(dx)=(y(x+y^3))/(x(y^3-x)) and ...

    Text Solution

    |

  15. The solution of differential equation (x+y(dy)/(dx))/(y-x(dy)/(dx)) ...

    Text Solution

    |

  16. The solution of the differential equation (dy)/(dx)=(3x^2y^4+2x y)/(x^...

    Text Solution

    |

  17. The solution of the differential equation {1+xsqrt((x^2+y^2))}dx+{sqrt...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. If dy/dx=(e^y-x)^(-1), where y(0)=0 , then y is expressed explicitly...

    Text Solution

    |