Find the particular solution of the ODE in this form: y" + 7 y = 6 e^x, with initial conditions y(0) = 7.8 and y' (0) = 6.7. What is the value of y at x = 5?

According to the solution in Exercise 58 of the differential equation for Newtons law of cooling, what happens to the temperature of an object after it has been in a surrounding medium with constant temperature for a long period of time? How well does this agree with reality?

If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per second. What is the terminal velocity, and how long does it take the filter to reach 99 of terminal velocity? Use a table increment of 0.1 and given your answer to the nearest tenth of a second.