Exercises

The first three questions require a yes or no answer while the last requires a more lengthy solution

1. Is this a linear first order ODE?
   

   NO because the unknown function appears in a cosine function which is not a linear function.

2. Is this a linear first order ODE?
   

   YES because the unknown function f(t) appears only to the first power.
   

3. Is this a linear first order ODE?
   

   YES because the unknown function f(t) appears only to the first power. But be careful to first rearrange the ODE in our notation in the discussion. Thus

4. What is the solution of the following linear first order ODE?
   

   Solution: Put the equation in our preferred notation and identify p(s) and g(s).
   
   
   Next
   
   Putting this together
   or
   Now use the initial condition to find the constant c.
   
   . Thus