I tried this differential equation out, and it worked:

This is not separable. However, if I write it as follows:

.

This equation has the form of aBernoulli's Equation(I cover this in my Differential Equations Tutorial):

(general form of Bernoulli Equation)

If we make a substitution the Bernoulli Eqn will become a linear equation we know how to solve.

We also need a substitution for .

We can get this by applying a definition of the chain rule: .

Substituting this into the DE, we get:

Multiply both sides by to get a linear DE:

Apply Integrating factor:

It should be known by now: when we multiply through by the int. factor, we get on the left side of the equation the derivative of

Thus, our DE becomes:

Solving the DE, we get:

We don't want v. We want y. So sub back in

When , we have:

I believe in this case and

Thus,

Since y(2)=50, we see that

My calculator tells me that

Thus, .

Now find t when y(t)=80

.

So at1 PM, 80 students will have heard the rumor.

(I hope my math was right! It does make sense!)

Hope this answered your question!