dy dx p x y q x show that y x ye x yp x is a general solution of dy dx

Question

dy/dx + P(x) y = Q(x). Show that y(x) = ye(x) + yp(x)
is a general solution of dy/dx + P(x) y = Q(x).
32. (a) Find constants A and B such that y, (x) = A sin x +
B cos x is a solution of dy/dx + y = 2 sinx. (b) Use the
result of part (a) and the method of Problem 31 to find the
general solution of dy/dx + y = 2 sinx. (c) Solve the
initial value problem dy/dx + y = 2 sinx, y(0) = 1.
33. A tank contains 1000 liters (L) of a solution consisting of
100 kg of salt dissolved in water. Pure water is pumped
into the tank at the rate of 5 L/s, and the mixture-kept
uniform by stirring— is pumped out at the same rate. How
long will it be until only 10 kg of salt remains in the tank?
34. Consider a reservoir with a volume of 8 billion cubic feet
(ft³) and an initial pollutant concentration of 0.25%. There
is a daily inflow of 500 million ft³ of water with a pollu-
tant concentration of 0.05% and an equal daily outflow of
the well-mixed water in the reservoir How long will it