Math 275
Exam 1
Show all your Steps to Receive Full Credit.
1.Find the solution of the initial value problem. Write the answer in explicit
form.
et ,
y
y0
1
1 y
2.-
Find the solution to the initial value problem:
x
3.-
(a)
(b)
2te
cos t
,
x0
1.
Show that the given equation is homogeneous.
Solve the differential equation.
dy
dx
4.-
x sin t
x2
x2
y2
xy
Show that the equation is exact, then solve the differential equation:
2
ye xy dx
xe xy
2y dy
0,
5.A tank contains 20 kg of salt dissolved in 5000 L of water. Brine that
contains 0.03 Kg of salt per liter of water enters the tank at a rate of 25 L per
minute. The solution is kept thoroughly mixed and drains from the tank at the
same rate. a) Find the amount of salt at any time t. b) How much salt
remains in the tank after half an hour?
1