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

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

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?

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 70^oF. Two hours later, the detective measured the body temperature again and found it to be 60^oF. If the room temperature is 50^oF, and assuming that the body temperature of the person before death was 98.6^oF, at what time did the murder occur? [log(2.43) = 0.88789; log(0.5)=-0.69315]

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.