07.01 Solutions of Differential Equations

Which order of steps adequately verifies that y2 = 2x − 1 is a solution to y times dy over dx equals 1? Step 1: dy over dx equals 1 over y Step 2: 2 times y times dy over dx equals 2 Step 3: 2 times y times one over y equals 2 Step 4: 2 = 2

2, 1, 3, 4

The position of a plane in motion is given by s(t), where t is measured in minutes. What relationship of the plane's flight is modeled by the differential equation s″ = 3t for 0 ≤ t ≤ 15?

During the first 15 minutes of flight, the plane's acceleration is directly proportional to time.

What is a possible solution to 2yy ′ = 12xy − 2ysinx? 1 y = 3x2 + cosx + 2 2 y = 3x2 + cosx − 1 3 y = 3x2 − cosx + 2

NOT - I only CONFIRMED ANSWER - I and II only

A heat source is removed from a thermal tile, causing the temperature to drop. If the rate of change of the temperature T of a thermal tile is inversely proportional the square root of time t, where t ≥ 0, write a differential equation that models the situation.

dT over dt equals negative c over the square root of t

Find a general solution to the differential equation dy over dx equals 4 over the square root of the quantity 4 minus x squared.

y equals 4 arcsin of quantity x over 2 close quantity plus C sub 1