Home
Class 12
MATHS
Find the integral curve of the different...

Find the integral curve of the differential equation, `x(1–x lny). Dy/dx +y =0` which passes through (1,1/e).

Text Solution

Verified by Experts

The correct Answer is:
x(ey + ln y + 1) = 1
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATION

    MOTION|Exercise Exercise 4|29 Videos

  • DIFFERENTIAL EQUATION

    MOTION|Exercise Exercise 2|48 Videos

  • DIFFERENTIABILITY

    MOTION|Exercise Exercise - 4 | Level-I Previous Year | JEE Main|15 Videos

  • ELLIPSE

    MOTION|Exercise Exercise - 4 | Level-I Previous Year | JEE Main|20 Videos

Similar Questions

Explore conceptually related problems

The solution curve of the differential equation, (1+e^(-x))(1+y^(2))(dy)/(dx)=y^(2) , which passes through the point (0,1), is:

The integrating factor of the differential equation (dy)/(dx) -y = x is e ^(-x)

The integrating factor of the differential equation (dy)/(dx)=1/(x+y+2) is

Let a curve satisfying the differential equation y^(2)dx=(x-(1)/(y))dy=0 which passes through (1,1) if the curve also passes through (k,2) then value of k is

The integrating factor of the differential equation (dy)/(dx)+y=(1+y)/(x) , is

The curve amongst the family of curves, represented by the differential equation (x^2-y^2)dx+2xydy=0 which passes through (1,1) is

An integrating factor of the differential equation (1+y+x^(2)y) dx + ( x +x^(3))dy = 0 is

The integrating factor of differential equation (dy)/(dx)+y=(1+y)/(x) is

Solution of the differential equation (x-y)(1-(dy)/(dx))=e^(x) is

MOTION-DIFFERENTIAL EQUATION -Exercise 3
  1. Consider the differential equation. Dy/dx +P(x)y = Q(x) (i) If two par...

    Text Solution

    |

  2. x(1+y^2)dx-y(1+x^2)dy =0

    Text Solution

    |

  3. Find the integral curve of the differential equation, x(1–x lny). Dy/d...

    Text Solution

    |

  4. A tank consists of 50 litres of fresh water. Two litres of brine each ...

    Text Solution

    |

  5. A normal is drawn at a point P(x , y) of a curve. It meets the x-ax...

    Text Solution

    |

  6. Find the curve for which the sum of the lengths of the tangent and sub...

    Text Solution

    |

  7. Find the curve y= f(x) where f(X) ge 0, f(0) =0,bounding a curvilinear...

    Text Solution

    |

  8. Find the equation of a curve such that the projection of its ordinate ...

    Text Solution

    |

  9. The light rays emanating from a point source situated at origin when r...

    Text Solution

    |

  10. The perpendicular from the origin to the tangent at any point on a cur...

    Text Solution

    |

  11. Find the curve for which any tangent intersects the y-axis at the poin...

    Text Solution

    |

  12. Find the curve such that the area of the trapezium formed by the co-or...

    Text Solution

    |

  13. Find the equation of the curve passing through the origin if the middl...

    Text Solution

    |

  14. A perpendicular drawn from any point P of the curve on the x-axis meet...

    Text Solution

    |

  15. The equation of curve in which portion of y-axis cutoff between origin...

    Text Solution

    |

  16. Find the orthogonal trajectories for the given family of curves when ‘...

    Text Solution

    |

  17. The population P of a town decreases at a rate proportional to the num...

    Text Solution

    |

  18. It is known that the decay rate of radium is directly proportional to ...

    Text Solution

    |

  19. Let the function ln f(x) is defined where f(x) exists for x geq 2 an...

    Text Solution

    |

  20. Find the differentiable function which satisfies the equation f(x)= -i...

    Text Solution

    |