( 20 pts)
MA241 Test 3 Spring 2020
Do the problems on the test in order, number questions, including parts, box your final answers and SHOW ALL WORK to receive credit. Read the directions carefully and follow all instructions. Good luck!!!
1. Find the general solution to the following differential equation. (x2 + 1) dy = xy
( 5 pts) ( 10 pts) ( 5 pts)
( 25 pts)
( 10 pts)
( 25 pts)
(c) Find the solution given the following initial conditions: y(0) = 4 and y′(0) = 5
3. Find the general solution of the equation y′′ − 3y′ + 2y = e3t.
4. State the form for the particular solution of the differential equation y′′ − 3y′ + 2y = sin 3x. Do not solve for any of the variables.
5. A tank contains 1000 L of brine (salt water) with 15 kg of dissolved salt. Pure water enters the tank at a rate of 10 L/min. The solution is kept throughly mixed and drains from the tank at the same rate. How much salt is in the tank after t minutes?
2. Given the differential equation below;
(a) State the auxiliary equation. (b) State the general solution.
dx
y′′ − 3y′ + 2y = 0