Home
Class 12
MATHS
A tank with a capacity of 1000 litres or...

A tank with a capacity of 1000 litres originally contains 100 gms of salt dissolved in 400 litres of water. Beginning at time t = 0 and ending at time t = 100 minutes, water containing 1 gm of salt per litre enters the tank at the rate of 4 litre/minute and the wheel mixed solution is drained from the tank at a rate of 2 litre/minute. Find the differential equation for the amount of salt y in the tank at time t.

Text Solution

Verified by Experts

The correct Answer is:
dy/dt = 4- y/200+t
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
MOTION-DIFFERENTIAL EQUATION -Exercise 3
  1. Find the curve for which any tangent intersects the y-axis at the poin...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. Find all functions f(x) defined on (-pi/2,pi/2) with real values and h...

    Text Solution

    |

  12. A tank contains 100 litres of fresh water. A solution containing 1 gm/...

    Text Solution

    |

  13. A tank with a capacity of 1000 litres originally contains 100 gms of s...

    Text Solution

    |

  14. (dy)/(dx)=y+int0^1 ydx given y=1 where x=0

    Text Solution

    |

  15. Find the continuous function which satisfies the relation, int0^x t f(...

    Text Solution

    |

  16. A curve passing through (1, 0) such that the ratio of the square of th...

    Text Solution

    |

  17. The curve f(x) is given by

    Text Solution

    |

  18. The curve g(x) is given by -

    Text Solution

    |

  19. The value of int1^2(g(x) -f(x))dx is-

    Text Solution

    |

  20. {:( " Column - I" , " Column - II") , ( "(A) A curve passing through...

    Text Solution

    |