In Problems 11 and 12 show that the substitution leads to a Bernoulli equation. Solve this equation (see Section 2.5).

Step-1:

In this problem we need to show that the substitution leads to a Bernoulli equation and then solve the equation .

Step-2:

Given equation is .

Substitute in above equation we get.

Now, the above equation is in the form of (which is Bernoulli equation).

Here, n = 3.

Both sides divide with we get.

…..(1)

Step-3:

Substitute,

Substitute these values in equation (1) we get.

Integrating factor is

Step-4:

Multiply the equation both sides with we get.

Integrating on both sides we get.