MA241 Test 3Spring 2021Do the problems on the test in order, number questions, including parts, box your final answers and SHOWALL WORK to receive credit. Read the directions carefully and follow all instructions. Good luck!!!1.( 20 pts) The population of a certain type of fish in Jordan Lake grows at a rate that is proportional to it’ssize.(a) Write this as a differential equation with P(t) = population of fish at time, t, measured in weeks.(b) When there are 700 fish present in the lake, the population is growing at a rate of 20 fish perweek. Use this information to find the growth constant.(c) If the initial population is 200 fish, state the solution function, P(t), to the differential equation.2. Given the differential equation below;y00− 6y0+ 5y = 0(a)( 5 pts) State the auxiliary equation.(b)( 10 pts) State the general solution.(c)( 5 pts) Find the solution given the following initial conditions:y(0) = 4 and y0(0) = 53.( 25 pts) Find the general solution of the equation y00− 6y0+ 5y = et.4.( 10 pts) State the form for the particular solution of the differential equation y00− 6y0+ 5y = sin 2x. Do notsolve for any of the variables.5.( 25 pts) A tank contains 500 L of brine (salt water) with 10 kg of dissolved salt. Pure water enters the tankat a rate of 20 L/min. The solution is kept throughly mixed and drains from the tank at the samerate. How much salt is in the tank after t
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