In Exercises 1–22, solve the differential equation.


(1+eˣ) dy + (yeˣ + e⁻ˣ) dx = 0

Solving Initial Value Problems

Solve the initial value problems in Exercises 15–20.

(x+1) dy/dx - 2 (x² + x)y = exp(x²) / (x+1), x > -1, y(0) = 5

Solve the Bernoulli equations in Exercises 29–32.

y' - y = xy²

Solve the Bernoulli equations in Exercises 29–32.

x²y' + 2xy = y³

In Exercises 1–22, solve the differential equation.

xy' + 2y = 1 - x⁻¹

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.

dy + x(2y - e^(x-x²))dx = 0

41. Cooling soup Suppose that a cup of soup cooled from 90°C to 60°C after 10 min in a room where the temperature was 20°C. Use Newton’s Law of Cooling to answer the following questions.

a. How much longer would it take the soup to cool to 35°C?

43. Surrounding medium of unknown temperature A pan of warm water (46°C) was put in a refrigerator. Ten minutes later, the water’s temperature was 39°C; 10 min after that, it was 33°C. Use Newton’s Law of Cooling to estimate how cold the refrigerator was.