engineering mathematics

2. Solve the differential equation y'=2_2 3. Find the solution using first order linear differential method: dy x2 + xy =x* cosx dx 4. Prof Atham starts an experiment using bacteria with a population of 200. It is found that the rate of population growth of the bacteria.my is given by = 0.04y where y is the population at time t minutes after the experiment starts. a) Find an expression for y, where y is the function of t. b) Estimate the population of the bacteria 1 hour after the experiment starts. 5. Protactinium-234" has a half-life of 70 minutes. If 150 grams of this element present initially, calculate the mass of that radioactive element after an hour. 6. The body of a murder victim with a body temperature 29C is found in a room that is kept at a constant temperature 15C. Two hours later, the temperature has decreased to 24C. If the body was found at 12 midnight and assume that the temperature of the body has cooled in accord with Newton's law, determine the time of death. (Given that the normal body temperature is 37C)