In Exercises 1–22, solve the differential equation.
x dy + (3y - x⁻² cos x) dx = 0, x > 0

In Exercises 1–22, solve the differential equation.

y' = xeʸ√(x-2)

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

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

In Exercises 1–22, solve the differential equation.

(x + 3y²) dy + y dx = 0 (Hint: d(xy) = y dx + x dy)

In Exercises 1–22, solve the differential equation.

xy' + 2y = 1 - x⁻¹

Solve the homogeneous equations in Exercises 5–10. First put the equation in the form of a homogeneous equation.

(x sin y/x - y cos y/x)dx + (x cos y/x) dy = 0

In Exercises 1–22, solve the differential equation.

sec x dy + x cos² y dx = 0