PROBLEM 21E

Each DE in Problems 15–22 is a Bernoulli equation.

In Problems 21 and 22 solve the given initial-value problem.

Solution:Step 1</p>

In this problem we need to solve the given initial value problem.

Step 2</p>

First we arranging the differential equation to change it to the standard form of bernoulli's equation i.e. by dividing both sides by , we get

Dividing both sides by , we get

To solve this we make the substitution .

Differentiating with respect to y, we get

From above equation we get .

We can write as follows

Step 3</p>

Substituting and in the differential equation , we get

Multiplying both sides by , we get

The equation is not in the standard form of bernoulli’s equation. To calculate the integrating factor, we do as follows