In Exercises 1–22, solve the differential equation.


y' = sin³ x cos² y

In Exercises 1–22, solve the differential equation.

dy + x(2y - e^(x-x²))dx = 0

In Exercises 23–28, solve the initial value problem.

y dx + (3x - xy + 2)dy = 0, y(2) = -1, y < 0

In Exercises 43 and 44, let S represent the pounds of salt in a tank at time t minutes. Set up a differential equation representing the given information and the rate at which S changes. Then solve for S and answer the particular questions.

Pure water flows into a tank at the rate of 4 gal/min, and the well-stirred mixture flows out of the tank at the rate of 5 gal/min. The tank initially holds 200 gal of solution containing 50 pounds of salt.

b. How many pounds of salt are in the tank after 1 minute? after 30 minutes?

In Exercises 1–22, solve the differential equation.

y' = xeˣ⁻ʸ csc y

In Exercises 1–22, solve the differential equation.

y' = (y²-1)x⁻¹

In Exercises 1–22, solve the differential equation.

x dy - (x⁴ - y) dx = 0