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12th Standard English Medium Maths Subject Ordinary Differential Equations Book Back 5 Mark Questions with Solution Part - II

12th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 25

    5 Marks

    5 x 5 = 25
  1. Solve the Linear differential equation:
    \(\frac { dy }{ dx } +\frac { y }{ x } =sinx\)

  2. Solve the Linear differential equation:
    \(({ x }^{ 2 }+1)\frac { d }{ y } dx+2xy=\sqrt { { x }^{ 2 }+4 } \)

  3. The growth of a population is proportional to the number present. If the population of a colony doubles in 50 years, in how many years will the population become triple?

  4. In a murder investigation, a corpse was found by a detective at exactly 8 p.m. Being alert, the detective also measured the body temperature and found it to be 70oF. Two hours later, the detective measured the body temperature again and found it to be 60oF. If the room temperature is 50oF, and assuming that the body temperature of the person before death was 98.6oF, at what time did the murder occur? [log(2.43) = 0.88789; log(0.5)=-0.69315]

  5. A tank initially contains 50 litres of pure water. Starting at time t = 0 a brine containing with 2 grams of dissolved salt per litre flows into the tank at the rate of 3 litres per minute. The mixture is kept uniform by stirring and the well-stirred mixture simultaneously flows out of the tank at the same rate. Find the amount of salt present in the tank at any time t > 0.

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