1. The problem statement, all variables and given/known data From a height of 18 meters above ground, an object is thrown vertically upwards at a speed of 30m/s. Find the equation where height h depends on time t. Find the maximum height of the object. 2. Relevant equations h=h0+v0t-(gt^2)/2 3. The attempt at a solution The equation of motion of an object thrown vertically upwards is h=h0+v0t-(gt^2)/2 By inserting h0=18 and v0=30 we get [itex]h=18+30t-(gt^2)/2[/itex], which is the correct answer. When t=3, h is max at 63. Now my problem here is that instead of finding the aforementioned equation of motion in a book, i was supposed to create it myself, using differential equation methods. How?