See the attached file for questioins

1.         Verify that  is a solution to the differential equation  

2.         Given the solution  to the differential equation .

            Find the constants C₁ and C₂ under the initial conditions  and

3.         Solve the differential equation  

4.         Find the particular solution that satisfies the initial condition.

            Differential equation:    Initial condition:  

5.         Solve the homogeneous differential equation  by making

            the appropriate substitution.

6.         The temperature of an object is 98 degrees Fahrenheit when brought into a room             that is 65 degrees. Four minutes later the object cools down to 88 degrees

            Fahrenheit. If the temperature of the room remains constant, how long will it take

            the object to cool down to 70 degrees Fahrenheit? (Hint: Use Newton’s Law of

            Cooling)

7.         Solve the differential equation with the initial condition by finding an integrating             factor.